Showing papers in "Tohoku Mathematical Journal in 2014"
TL;DR: In this paper, it was shown that the set of points for which the Birkhoff averages of a continuous function diverge is residual for topologically transitive topological Markov chains, sofic shifts and more generally shifts with specification.
Abstract: For shifts with weak specification, we show that the set of points for which the Birkhoff averages of a continuous function diverge is residual. This includes topologically transitive topological Markov chains, sofic shifts and more generally shifts with specification. In addition, we show that the set of points for which the Birkhoff averages of a continuous function have a prescribed set of accumulation points is also residual. The proof consists of bridging together strings of sufficiently large length corresponding to a dense set of limits of Birkhoff averages. Finally, we consider intersections of finitely many irregular sets and show that they are again residual. As an application, we show that the set of points for which the Lyapunov exponents on a conformal repeller are not limits is residual.
31 citations
TL;DR: In this article, a complete classification of four-dimensional conformally flat homogeneous pseudo-Riemannian manifolds is given, and the classification is extended to a complete class of 4D conformal flat manifold classes.
Abstract: We obtain a complete classification of four-dimensional conformally flat homogeneous pseudo-Riemannian manifolds.
17 citations
TL;DR: Bilinear Fourier multiplier operators corresponding to multipliers that are singular at the origin are considered in this article, and new criterions on such multipliers to assure the boundedness of the corresponding operators from $L^p \times L^q$ to $L€r, $1/p+1/q=1/r, are given in the range $1
Abstract: Bilinear Fourier multiplier operators corresponding to multipliers that are singular at the origin are considered. New criterions on such multipliers to assure the boundedness of the corresponding operators from $L^p \times L^q$ to $L^r$, $1/p+1/q=1/r$, are given in the range $1
16 citations
TL;DR: In this paper, the Ricci operator on a contact Riemannian 3-manifold is invariant along the Reeb flow if and only if $M$ is Sasakian or locally isometric to
Abstract: We prove that the Ricci operator on a contact Riemannian 3-manifold $M$ is invariant along the Reeb flow if and only if $M$ is Sasakian or locally isometric to $\mathrm{SU}(2)$ (or $\mathrm{SO}(3)$), $\mathrm{SL}(2,\boldsymbol{R})$ (or $O(1,2)$), the group $E(2)$ of rigid motions of Euclidean 2-plane with a contact left invariant Riemannian metric
11 citations
TL;DR: For the multisublinear maximal operator on martingale spaces, the authors characterized the weights for which the maximal operator is bounded from a constant to a constant, and showed that the bilinear version of one-weight theory partially holds.
Abstract: Let $v, \omega_1, \omega_2$ be weights and let $1
11 citations
TL;DR: In this paper, Kobayashi generalized the theory of Coleman power series to general groups of elliptic curves and applied it to a study of $p$-adic height pairings.
Abstract: Shinichi Kobayashi found a generalization of the Coleman power series theory to formal groups of elliptic curves and applied it to a study of $p$-adic height pairings. In this paper, we generalize his theory of Coleman power series to general formal groups.
10 citations
TL;DR: In this article, an ergodic, essentially free and measure-preserving action of a non-amenable Baumslag-Solitar group on a standard probability space is associated with a flow.
Abstract: To an ergodic, essentially free and measure-preserving action of a non-amenable Baumslag-Solitar group on a standard probability space, a flow is associated. The isomorphism class of the flow is shown to be an invariant of such actions of Baumslag-Solitar groups under weak orbit equivalence. Results on groups which are measure equivalent to Baumslag-Solitar groups are also provided.
9 citations
TL;DR: In this paper, the existence, multiplicity and nonexistence of positive solutions for a parametric nonlinear Neumann problem driven by the $p$-Laplacian were studied.
Abstract: Using variational methods based on the critical point theory and suitable truncation and comparison techniques, we study existence, multiplicity and nonexistence of positive solutions for a parametric nonlinear Neumann problem driven by the $p$-Laplacian. Our hypotheses cover the case of nonlinearities of concave-convex type whose exponents depend on the parameter.
8 citations
TL;DR: In this paper, the 4-th multiple residue symbol $[p_1, p_2,p_3,p _4] was introduced for certain four prime numbers $p_i$'s, which extends the Legendre symbol and the Redei triple symbol.
Abstract: In this paper, we introduce the 4-th multiple residue symbol $[p_1,p_2,p_3,p_4]$ for certain four prime numbers $p_i$'s, which extends the Legendre symbol $\big(\frac{p_1}{p_2}\big)$ and the Redei triple symbol $[p_1,p_2,p_3]$ in a natural manner. For this we construct concretely a certain nilpotent extension $K$ over $\boldsymbol{Q}$ of degree 64, where ramified prime numbers are $p_1, p_2$ and $p_3$, such that the symbol $[p_1,p_2,p_3,p_4]$ describes the decomposition law of $p_4$ in the extension $K/\boldsymbol{Q}$. We then establish the relation of our symbol $[p_1,p_2,p_3,p_4]$ and the 4-th arithmetic Milnor invariant $\mu_2(1234)$ (an arithmetic analogue of the 4-th order linking number) by showing $[p_1,p_2,p_3,p_4] = (-1)^{\mu_2(1234)}$.
8 citations
TL;DR: In this paper, Cheng-Yau type local gradient estimate for harmonic functions on Alexandrov spaces with Ricci curvature bounded below was proved for the case of negative Ricci lower bound.
Abstract: In this note, we prove Cheng-Yau type local gradient estimate for harmonic functions on Alexandrov spaces with Ricci curvature bounded below. We adopt a refined version of Moser's iteration which is based on Zhang-Zhu's Bochner type formula in "Yau’s gradient estimates on Alexandrov spaces." Our result improves the previous one of Zhang-Zhu in the case of negative Ricci lower bound.
7 citations
TL;DR: In this paper, the singular integral with rough kernel associated to surfaces is studied and bounded under a sharp size condition on its kernels in an extrapolation argument, and the corresponding results for maximal truncated singular integral operators are also established.
Abstract: This paper is devoted to studying the singular integral with rough kernel associated to surfaces, which contain many classical surfaces as model examples. Also, the kernel of our operator lacks smoothness on the unit sphere as well as in the radial direction. We obtain the $L^p$ boundedness of the singular integral under a sharp size condition on its kernels in an extrapolation argument. In addition, the corresponding results for maximal truncated singular integral operators are also established.
TL;DR: In this paper, the solvability of perturbed variational inequalities involving the operator $T+S$ and the function $\phi$ has been studied and the associated range results for nonlinear operators are also given.
Abstract: Let $X$ be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space $X^*,$ and let $K$ be a nonempty, closed and convex subset of $X$ with $0$ in its interior. Let $T$ be maximal monotone and $S$ a possibly unbounded pseudomonotone, or finitely continuous generalized pseudomonotone, or regular generalized pseudomonotone operator with domain $K$. Let $\phi$ be a proper, convex and lower semicontinuous function. New results are given concerning the solvability of perturbed variational inequalities involving the operator $T+S$ and the function $\phi$. The associated range results for nonlinear operators are also given, as well asextensions and/or improvements of known results of Kenmochi, Le, Browder, Browder and Hess, De Figueiredo, Zhou, and others.
TL;DR: In this article, the authors considered the relativistic α-stable Markov process with a symmetric function and described the frequency of jump from x to y, and showed that if J(x,y) 1/|x− y|d+α holds for some 0 0, then the associated Markov processes are relativistically stable.
Abstract: Here J(x,y) is a symmetric function and describes the frequency of jump from x to y. In particular, if J(x,y) 1/|x− y|d+α holds for some 0 0, we call the associated Markov process relativistic α-stable-like. In the sequel, we deal with these two kinds of jump Markov process.
TL;DR: In this paper, a family of stable McKay quiver representations on the Danilov resolution of the singularity was constructed and the resolution is the normalization of the coherent component of the fine moduli space for a suitable stability condition.
Abstract: We construct a family of McKay quiver representations on the Danilov resolution of the $\frac{1}{r}(1,a,r-a)$ singularity. This allows us to show that the resolution is the normalization of the coherent component of the fine moduli space of $\theta$-stable McKay quiver representations for a suitable stability condition $\theta$. We describe explicitly the corresponding union of chambers of stability conditions for any coprime numbers $r,a$.
TL;DR: In this paper, a Cartan type identity for curvature-adapted isoparametric hypersurfaces in symmetric spaces of compact type or non-compact type was obtained.
Abstract: In this paper, we obtain a Cartan type identity for curvature-adapted isoparametric hypersurfaces in symmetric spaces of compact type or non-compact type. This identity is a generalization of Cartan-D'Atri's identity for curvature-adapted (=amenable) isoparametric hypersurfaces in rank one symmetric spaces. Furthermore, by using the Cartan type identity, we show that certain kind of curvature-adapted isoparametric hypersurfaces in a symmetric space of non-compact type are principal orbits of Hermann actions.
TL;DR: In this paper, a generalization of classical Finsler structures has been introduced by R. Bryant by defining the notion of (I;J;K)-generalized FINsler structures, which can be defined in any dimension.
Abstract: This is a joint work with Sorin V. Sabau and Gheorghe Pitis. A classical Finsler structure (M;F) is a smooth manifold M endowed with a Banach norm on each tangent space TxM that varies smoothly with the base point all over the manifold, for any x 2 M. A Riemannian manifold is a particular case when each of these Banach norms are induced by a quadratic form. Geometrically, this is equivalent to the choice of a unit sphere in each tangent space, such that one obtains a smooth hypersurface § ‰ TM which has the property that each fiber §x := § \ TxM is a smooth, strictly convex hypersurface in TM which surrounds the origin Ox 2 TxM. Except the preference for local computations, a peculiarity of Finsler structures is that, unlike the Riemannian case, one has no means to specify a canonical Finsler structure on a given manifold, therefore, constructing models for Finslerian struc- tures with given geometrical properties (such as constant flag curvature) is an im- portant topic that rises interesting questions about the local and global generality of such structures. A generalization of classical Finsler structures has been introduced by R. Bryant by defining the notion of (I;J;K)-generalized Finsler structures (see (3)), namely a 3-manifold § endowed with a coframing ! = f!1;!2;!3g satisfying d! 1 = iI! 1 ^ ! 3 + ! 2 ^ ! 3 d! 2 = i! 1 ^ ! 3 d! 3 = K! 1 ^ ! 2 i J! 1 ^ ! 3 : We use here only such structures on 3-manifolds, but these can be defined in any dimension (see (4)). Generalized Finsler structures were introduced with the specific intention of 'micro-localization' of classical Finsler structures that allows separating the local geometrical properties of coframes satisfying certain dierential geometric conditions, or solving PDE's, from the global geometrical properties of the manifolds § or M related with the behavior of the leaf space of certain foliations. There are a lot of questions and problems that this new notion brings about. For instance, the absence of results on the existence of global defined Finsler structures motivates one to study the existence of global defined generalized Finsler struc- tures on a 3-manifold § as well as the case when this is realizable as a classical Finsler structure on a surface M. For the case of constant flag curvature one, the only available constructions are Bryant's. In particular, making use of generalized Finsler structures, he was able to construct for the first time global defined Finsler 1
TL;DR: In this paper, a functor from the category of quasi-coherent sheaves on a variety $X$ which admits a Cox ring was introduced, which preserves torsion-freeness and reflexivity.
Abstract: For a variety $X$ which admits a Cox ring, we introduce a functor from the category of quasi-coherent sheaves on $X$ to the category of graded modules over the homogeneous coordinate
ring of $X$. We show that this functor is right adjoint to the sheafification functor and therefore left-exact. Moreover, we show that this functor preserves torsion-freeness and reflexivity. For the
case of toric sheaves, we give a combinatorial characterization of its right derived functors in terms of certain right derived limit functors.
TL;DR: In this article, the authors apply the result of H. Beirao da Veiga and C. J. Amick to prove the independence of such a condition on the particular domain.
Abstract: H. Beirao da Veiga proved that, for a straight channel in $\boldsymbol{R}^n$ ($n$ arbitarily large) and for a given flux with the time periodicity, there exists a unique time periodic Poiseuille flow in a straight channel in $\boldsymbol{R}^n$. Furthermore, the existence of a time periodic solution in a perturbed channel (Leray's problem) is shown for the Stokes problem (arbitary dimension) and for the Navier-Stokes problem ($n\le4$). Concerning the Navier-Stokes case, a quatitative condition requaired to show the existence of a time periodic solution depends not just on the flux of the time periodic Poiseuille flow but also on the domain it self. In this paper, by applying the result of H. Beirao da Veiga and C. J. Amick, we succeed in proving the independence of such a condition on the particular domain.
TL;DR: In this paper, a nonlinear parametric Dirichlet problem driven by a nonhomogeneous differential operator (special cases are the $p$-Laplacian and the $(p,q)$-differential operator) and with a reaction which has the combined effects of concave (($p-1)$)-sublinear) and convex ($(p)-superlinear) terms was considered.
Abstract: In this paper we consider a nonlinear parametric Dirichlet problem driven by a nonhomogeneous differential operator (special cases are the $p$-Laplacian and the $(p,q)$-differential operator) and with a reaction which has the combined effects of concave (($p-1)$-sublinear) and convex ($(p-1)$-superlinear) terms. We do not employ the usual in such cases AR-condition. Using variational methods based on critical point theory, together with truncation and comparison techniques and Morse theory (critical groups), we show that for all small $\lambda>0$ ($\lambda$ is a parameter), the problem has at least five nontrivial smooth solutions (two positive, two negative and the fifth nodal). We also prove two auxiliary results of independent interest. The first is a strong comparison principle and the second relates Sobolev and Holder local minimizers for $C^1$ functionals.
TL;DR: In this article, the authors studied the spectrum of the Finsler-Laplace operator for regular Hilbert geometries, defined by convex sets with C^2 boundaries.
Abstract: We study the spectrum of the Finsler--Laplace operator for regular Hilbert geometries, defined by convex sets with $C^2$ boundaries. We show that for an $n$-dimensional geometry, the spectral gap is bounded above by $(n-1)^2/4$, which we prove to be the infimum of the essential spectrum. We also construct examples of convex sets with arbitrarily small eigenvalues.
TL;DR: In this article, a torus equivariant blowup of a compact toric surface admits a cscK metric, where k is the number of equivariants of the torus.
Abstract: Let $X$ be a compact toric surface. Then there exists a sequence of torus equivariant blow-ups of $X$ such that the blown-up toric surface admits a cscK metric.
TL;DR: In this paper, it was shown that every real form of a hermitian symmetric space of compact type is a symmetric $R$-space and vice-versa.
Abstract: In 1984 Masaru Takeuchi showed that every real form of a hermitian symmetric space of compact type is a symmetric $R$-space and vice-versa. In this note we present a geometric proof of this result.
TL;DR: For an algebroid function in the unit disk of finite lower order with a deficient value, we can estimate its growth order in terms of the convergence exponent of the points of the deficient value and other distinct values not lying on a radial system.
Abstract: For an algebroid function in the unit disk of finite lower order with a deficient value, we can estimate its growth order in terms of the convergence exponent of the points of the deficient value and other distinct values not lying on a radial system and the maximal difference of the arguments of adjacent rays.
TL;DR: In this article, the Laguerre heat diffusion was shown to converge to a pointwise convergence in the Euclidean space with respect to a weight of order greater than or equal to 0.
Abstract: In this paper we get sharp conditions on a weight $v$ which allow us to obtain some weighted inequalities for a local Hardy-Littlewood Maximal operator defined on an open set in the Euclidean $n$-space. This result is applied to assure a pointwise convergence of the Laguerre heat-diffusion semigroup $u(x, t) = (T(t) f)(x)$ to $f$ when $t$ tends to zero for all functions $f$ in $L^{p}(v(x)dx)$ for $p$ greater than or equal to 1 and a weight $v$. In proving this we obtain weighted inequalities for the maximal operator associated to the Laguerre diffusion semigroup of the Laguerre differential operator of order greater than or equal to 0. Finally, as a by-product, we obtain weighted inequalities for the Riesz-Laguerre operators.
TL;DR: In this paper, the authors give explicit symplectic iso morphisms from the cotangent bundle of the complex generalized flag var ieties onto the complex coadjoint orbits.
Abstract: The purpose of this paper is to give explicit symplectic iso morphisms from the cotangent bundle of the complex generalized flag var ieties onto the complex coadjoint orbits. If we let the complex Lie group G act on the cotangent bundle by an affine transformation instead of the canonical one, we shall see that the isomorphism is G-equivariant.