Showing papers in "Tohoku Mathematical Journal in 2004"
TL;DR: In this article, all totally geodesic submanifolds of connected irreducible Riemannian symmetric spaces of noncompact type arise as a singular orbit of a cohomogeneity one action on the symmetric space.
Abstract: We classify all totally geodesic submanifolds of connected irreducible Riemannian symmetric spaces of noncompact type which arise as a singular orbit of a cohomogeneity one action on the symmetric space.
54 citations
TL;DR: In this article, the authors studied different notions of blow-up of a scheme along a subscheme, depending on the datum of an embedding of the scheme into an ambient scheme.
Abstract: We study different notions of blow-up of a scheme $X$ along a subscheme $Y$, depending on the datum of an embedding of $X$ into an ambient scheme The two extremes in this theory are the ordinary blow-up, corresponding to the identity, and the 'quasi-symmetric blow-up', corresponding to the embedding of $X$ into a nonsingular variety We prove that this latter blow-up is intrinsic of $Y$ and $X$, and is universal with respect to the requirement of being embedded as a subscheme of the ordinary blow-up of some ambient space along~$Y$ We consider these notions in the context of the theory of characteristic classes of singular varieties We prove that if $X$ is a hypersurface in a nonsingular variety and $Y$ is its 'singularity subscheme', these two extremes embody respectively the conormal and characteristic cycles of $X$ Consequently, the first carries the essential information computing Chern-Mather classes, and the second is likewise a carrier for Chern-Schwartz-MacPherson classes In our approach, these classes are obtained from Segre class-like invariants, in precisely the same way as other intrinsic characteristic classes such as those proposed by Fulton, and by Fulton and Johnson We also identify a condition on the singularities of a hypersurface under which the quasi-symmetric blow-up is simply the linear fiber space associated with a coherent sheaf
44 citations
TL;DR: In this article, a determinant expression for a family of classical transcendental solutions of the Painleve V and VI equations is presented, along with a degeneration of these solutions along the process of coalescence for the painleve equations.
Abstract: We present a determinant expression for a family of classical transcendental solutions of the Painleve V and the Painleve VI equation. Degeneration of these solutions along the process of coalescence for the Painleve equations is discussed.
42 citations
TL;DR: In this article, a new elementary proof of the global or almost global existence theorem of S. Klainerman and T. Sideris has been given, which is carried out in line with S. Sogge's theorem.
Abstract: We give a new, elementary proof of the global or almost global existence theorem of S. Klainerman. Our result also covers the almost global existence theorem of M. Keel, F. Smith, and C. D. Sogge. The proof is carried out in line with S. Klainerman and T. C. Sideris.
40 citations
TL;DR: In this paper, the continuous wavelet transform is extended to certain distributions and continuity results are obtained in a generalized Sobolev space, Besov space and Lizorkin-Triebel space.
Abstract: The continuous wavelet transform is extended to certain distributions and continuity results are obtained. Boundedness results in a generalized Sobolev space, Besov space and Lizorkin-Triebel space are given.
31 citations
TL;DR: In this article, the authors studied normal subgroups of Kleinian groups as well as discrepancy groups (d-groups), which are groups for which the exponent of convergence is strictly less than the Hausdorff dimension of the limit set.
Abstract: In this paper we study normal subgroups of Kleinian groups as well as discrepancy groups (d-groups), that are Kleinian groups for which the exponent of convergence is strictly less than the Hausdorff dimension of the limit set. We show that the limit set of a d-group always contains a range of fractal subsets, each containing the set of radial limit points and having Hausdorff dimension strictly less than the Hausdorff dimension of the whole limit set. We then consider normal subgroups $G$ of an arbitrary non-elementary Kleinian group $H$, and show that the exponent of convergence of $G$ is bounded from below by half of the exponent of convergene of $H$. Finally, we give a discussion of various examples of d-groups.
30 citations
TL;DR: In this paper, the authors generalize Roberts' counterexample to the fourteenth problem of Hilbert, and give a sufficient condition for certain invariant rings not to be finitely generated.
Abstract: We generalize Roberts' counterexample to the fourteenth problem of Hilbert, and give a sufficient condition for certain invariant rings not to be finitely generated. It shows that there exist a lot of counterexamples of this type. We also determine the initial algebra of Roberts' counterexample for some monomial order
21 citations
TL;DR: For a complex minimal smooth projective surface of general type, it was shown in this paper that any automorphism group inducing trivial actions on the second rational cohomology of the projective surfaces is isomorphic to a cyclic group of order less than five or the product of two groups of order two, provided that the Euler characteristic of the structure sheaf is larger than $188.
Abstract: It is proved that, for a complex minimal smooth projective surface $S$ of general type, any automorphism group of $S$, inducing trivial actions on the second rational cohomology of $S$, is isomorphic to a cyclic group of order less than five or the product of two groups of order two, provided that the Euler characteristic of the structure sheaf of $S$ is larger than $188$.
19 citations
18 citations
TL;DR: In this paper, the intersection numbers of loaded cycles associated with an $n$-fold Selberg-type integral were evaluated using high-dimensional local systems, and the intersection number was shown to be a function of the number of cycles in the system.
Abstract: We evaluate the intersection numbers of loaded cycles associated with an $n$-fold Selberg-type integral. We proceed inductively using high-dimensional local systems.
16 citations
TL;DR: In this paper, the authors study positive Toeplitz operators between the harmonic Bergman spaces and give characterizations of bounded and compact operators taking one Bergman space into another in terms of certain Carleson measures.
Abstract: On the setting of bounded smooth domains, we study positive Toeplitz operators between the harmonic Bergman spaces. We give characterizations of bounded and compact Toeplitz operators taking one harmonic Bergman space into another in terms of certain Carleson and vanishing Carleson measures.
TL;DR: In this article, the authors studied the Kirchhoff elastic rods in the three-sphere of constant curvature, and gave explicit expressions of the elastic rod in terms of elliptic functions and integrals.
Abstract: The Kirchhoff elastic rod is one of the mathematical models of thin elastic rods, and is a critical point of the energy functional with the effect of bending and twisting. In this paper, we study Kirchhoff elastic rods in the three-sphere of constant curvature. In particular, we give explicit expressions of Kirchhoff elastic rods in terms of elliptic functions and integrals. In addition, we obtain equivalent conditions for Kirchhoff elastic rods to be closed, and give an example of closed Kirchhoff elastic rods.
TL;DR: In this paper, it was shown that the induced representation from a square integrable irreducible representation is irrreducibly irrharducible for non-zero characteristic.
Abstract: Deligne, Kazhdan and Vigneras proved that, for an inner form of $GL_n$ over a zero characteristic $p$-adic field, the induced representation from a square integrable irreducible representation is irrreducible. Here we prove the case of non-zero characteristic.
TL;DR: In this paper, the authors completely classified Lagrangian H -umbilical surfaces of constant curvature in complex Euclidean plane and proved that they are Lagrangians.
Abstract: In this article we completely classify Lagrangian H -umbilical surfaces of constant curvature in complex Euclidean plane.
TL;DR: In this paper, a limiting uniqueness criterion in terms of the vorticity for the Navier-Stokes equations in the Besov space was investigated, and it was shown that Leray-Hopf's weak solution is unique under an auxiliary assumption that the V2V belongs to a scale characterized by the BMO in space and the Orlicz space in time direction.
Abstract: We investigate a limiting uniqueness criterion in terms of the vorticity for the Navier-Stokes equations in the Besov space. We prove that Leray-Hopf's weak solution is unique under an auxiliary assumption that the vorticity belongs to a scale characterized by the Besov space in space, and the Orlicz space in time direction. As a corollary, we give also the uniqueness criterion in terms of bounded mean oscillation (BMO).
TL;DR: In this paper, the authors construct meromorphic data and prove a representation theorem for mean curvature one conformal immersions into the hyperbolic three-space and give various examples.
Abstract: In this paper we construct meromorphic data and prove a representation theorem for mean curvature one conformal immersions into the hyperbolic three-space. We also give various examples.
TL;DR: In this article, a generalization of Kohnen-Zagier's results concerning Fourier coefficients of modular forms of half integral weight belonging to KohnEN's spaces is presented.
Abstract: The purpose of this paper is to derive a generalization of Kohnen-Zagier's results concerning Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces, and to refine our previous results concerning Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces. Employing kernel functions, we construct a correspondence $\varPsi$ from modular forms of half integral weight $k+1/2$ belonging to Kohnen's spaces to modular forms of weight $2k$. We explicitly determine the Fourier coefficients of $\varPsi(f)$ in terms of those of $f$. Moreover, under certain assumptions about $f$ concerning the multiplicity one theorem with respect to Hecke operators, we establish an explicit connection between the square of Fourier coefficients of $f$ and the critical value of the zeta function associated with the image $\varPsi(f)$ of $f$ twisted with quadratic characters, which gives a further refinement of our results concerning Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces.
TL;DR: In this paper, a complete list of the monodromies of degenerations of genus three which are not realized as the monodes of any hyperelliptic families of genus 3 is given.
Abstract: A complete list of the monodromies of degenerations of genus three which are not realized as the monodromies of any hyperelliptic families of genus three is given. We also prove that all the other monodromies of genus three are realized as the monodromies of certain hyperelliptic families.
TL;DR: In this article, the existence of complete orientable minimal surfaces with finite total curvature in Euclidean three-space is studied. And for any positive genus, it is shown that there exist noncongruent examples having the same symmetry group and conformal type.
Abstract: Concerning complete orientable minimal surfaces with finite total curvature in Euclidean three-space, we show for any positive genus the existence of noncongruent examples having the same symmetry group and conformal type
TL;DR: In this paper, it was shown that there exists no stable hypersurface of an n-euclidean space with vanishing (n − 1)-mean curvature and zero Gauss-Kronecker curvature, provided the immer- sion is proper and the total curvature is finite.
Abstract: A form of Bernstein theorem states that a complete stable minimal surface in euclidean space is a plane. A generalization of this statement is that there exists no com- plete stable hypersurface of an n-euclidean space with vanishing (n − 1)-mean curvature and nowhere zero Gauss-Kronecker curvature. We show that this is the case, provided the immer- sion is proper and the total curvature is finite.
TL;DR: The notion of relative log schemes with boundary was introduced in this article, which is a morphism of log schemes together with a (log schematically) dense open immersion of its source into a third log scheme.
Abstract: We introduce the notion of a relative log scheme with boundary: a morphism of log schemes together with a (log schematically) dense open immersion of its source into a third log scheme. The sheaf of relative log differentials naturally extends to this compactification and there is a notion of smoothness for such data. We indicate how this weak sort of compactification may be used to develop useful de Rham and crystalline cohomology theories for semistable log schemes over the log point over a field which are not necessarily proper.
TL;DR: In this paper, it was shown that the conjecture that the boundary quasiextremal distance constant of a Jordan domain is not true for all asymptotically conformal extension domains other than disks.
Abstract: Given a Jordan domain $\Omega$ in the extended complex plane $\overline{\kern-1.5pt\Bbb C}$, denote by $M_b(\Omega), M(\Omega)$ and $R(\Omega)$ the boundary quasiextremal distance constant, quasiextremal distance constant and quasiconformal reflection constant of $\Omega$, respectively. It is known that $M_b(\Omega)\le M(\Omega)\le R(\Omega)+1$. In this paper, we will give some further relations among $M_b(\Omega), M(\Omega)$ and $R(\Omega)$ by introducing and studying some other closely related constants. Particularly, we will give a necessary and sufficient condition for $M_b(\Omega)=R(\Omega)+1$ and show that $M(\Omega)
TL;DR: Two-weight Lp norm inequalities, uniform with respect to the order of the involved Bessel function, are proved for the Bochner-Riesz means of the first order for the Hankel transform as discussed by the authors.
Abstract: Two-weight Lp norm inequalities, uniform with respect to the order of the involved Bessel function, are proved for the Bochner-Riesz means of the first order for the Hankel transform. Both sufficient and necessary conditions for parameters used in the two weights are determined. The proof relies on uniform pointwise asymptotic estimates for the Bessel functions that were shown by Barcelo and Cordoba.
TL;DR: In this paper, the authors studied the mapping properties of multilinear oscillatory singular integral operators with polynomial phase and rough kernel and showed that for any non-trivial phase, the boundedness of these operators can be deduced from that of the corresponding local MISO operators.
Abstract: This paper is devoted to the study on the $L^p$-mapping properties for a class of multilinear oscillatory singular integrals with polynomial phase and rough kernel. By means of the method of block decomposition for the kernel function, the authors show that for any non-trivial polynomial phase, the $L^p(\rz)$ boundedness of the multilinear oscillatory singular integral operators and that of the corresponding local multilinear singular integral operators are equivalent; and for any real-valued polynomial phase, the $L^p(\rz)$ boundedness of the multilinear oscillatory integral operators can be deduced from that of the corresponding multilinear singular integral operators.
TL;DR: In this article, the authors classified semi-Riemannian submersions with connected totally geodesic fibres from a real pseudo-hyperbolic space onto a Riemannians manifold under the assumption that the dimension of the fibres is less than or equal to three.
Abstract: We classify semi-Riemannian submersions with connected totally geodesic fibres from a real pseudo-hyperbolic space onto a semi-Riemannian manifold under the assumption that the dimension of the fibres is less than or equal to three. Also, we obtain the classification of semi-Riemannian submersions with connected complex totally geodesic fibres from a complex pseudo-hyperbolic space onto a semi-Riemannian manifold under the assumption that the dimension of the fibres is less than or equal to two. We prove that there are no semi-Riemannian submersions with connected quaternionic fibres from a quaternionic pseudo-hyperbolic space onto a Riemannian manifold.
TL;DR: In this article, the validity of geometric optics for nonlinear wave equations in three dimensions whose solutions, pulse like, focus at a point was studied, where the amplitude of the initial data is sufficiently big, strong nonlinear effects occur.
Abstract: We study the validity of geometric optics in $L^\infty$ for nonlinear wave equations in three space dimensions whose solutions, pulse like, focus at a point. If the amplitude of the initial data is subcritical, then no nonlinear effect occurs at leading order. If the amplitude of the initial data is sufficiently big, strong nonlinear effects occur; we study the cases where the equation is either dissipative or accretive. When the equation is dissipative, pulses are absorbed before reaching the focal point. When the equation is accretive, the family of pulses becomes unbounded.
TL;DR: In this article, the extremal length of horizontal vector measures on a Carnot group and capacities associated with linear subelliptic equations were studied in domains with an intrinsic metric.
Abstract: We define the extremal length of horizontal vector measures on a Carnot group and study capacities associated with linear sub-elliptic equations. The coincidence between the definition of the p-module of horizontal vector measure system and two different definitions of the p-capacity is proved. We show the continuity property of a p-module generated by a family of horizontal vector measures. Reciprocal relations between the p-capacity and q-module ( 1/p+ 1/q = 1 ) of horizontal vector measures are obtained. A peculiarity of our approach consists of the study of the above mentioned notions in domains with an intrinsic metric.
TL;DR: In this article, it was shown that if a function mapping the real line to itself (and fixing the origin) operates by composition on the left to map the Dirichlet space into itself, then the function is necessarily locally Lipschitz continuous.
Abstract: In the context of a strongly local Dirichlet space we show that if a function mapping the real line to itself (and fixing the origin) operates by composition on the left to map the Dirichlet space into itself, then the function is necessarily locally Lipschitz continuous. If, in addition, the Dirichlet space contains unbounded elements, then the function must be globally Lipschitz continuous. The proofs rely on a co-area formula for condenser potentials.