Showing papers in "Tohoku Mathematical Journal in 2023"
TL;DR: In this article , the authors studied the bilinear estimates in the Sobolev spaces with the Dirichlet and Neumann boundary condition and showed that the optimal regularity is revealed to get such estimates in half space case, which is related to both smoothness of functions and boundary behavior.
Abstract: We study the bilinear estimates in the Sobolev spaces with the Dirichlet and the Neumann boundary condition. The optimal regularity is revealed to get such estimates in the half space case, which is related to not only smoothness of functions and but also boundary behavior. The crucial point for the proof is how to handle boundary values of functions and their derivatives.
TL;DR: In this article , the authors studied product manifolds with Finsler metrics arising from warped product structure and gave an equivalent condition for those metrics to be of quadratic Weyl curvature.
Abstract: The class of warped product manifolds plays an important role in differential geometry and physics. In this paper, we shall study product manifolds $\mathbb{R} \times M$ with Finsler metrics arising from warped product structure. We give an equivalent condition for those metrics to be of quadratic Weyl curvature.
TL;DR: In this paper , the authors studied the behavior of functions of bounded lower oscillation under the change of measure given by the weight, and provided sharp upper and lower bounds for the norm of the inclusion of a function in a treelike structure.
Abstract: The purpose of the paper is to study the behavior of the classes of functions of bounded lower oscillation under the change of measure given by the weight $w$. More specifically, we provide sharp upper and lower bounds for the norm of the inclusion $BLO\hookrightarrow BLO(w)$ in terms of $A_\infty$ constant of the weight. The results hold in the general context of probability spaces equipped with a treelike structure.
TL;DR: In this paper , a mass critical nonlinear Schrödinger equation with a real-valued potential is considered and a minimal mass solution that blows up at finite time is constructed under weaker assumptions on spatial dimensions and potentials.
Abstract: We consider a mass critical nonlinear Schrödinger equation with a real-valued potential. In this work, we construct a minimal mass solution that blows up at finite time, under weaker assumptions on spatial dimensions and potentials than Banica, Carles, and Duyckaerts (2011). Moreover, we show that the blow-up solution converges to a blow-up profile. Furthermore, we improve some parts of the arguments in Raphaël and Szeftel (2011) and Le Coz, Martel, and Raphaël (2016).
TL;DR: In this article , the authors studied nonorientable maximal surfaces in Lorentz-Minkowski 3-space and proved existence results for surfaces of this kind with high genus and one end.
Abstract: We study nonorientable maximal surfaces in Lorentz-Minkowski 3-space. We prove some existence results for surfaces of this kind with high genus and one end.
TL;DR: In this paper , the existence of quadratic relations between periods of meromorphic flat bundles on complex manifolds with poles along a divisor with normal crossings under the assumption of "goodness" was proved.
Abstract: We prove the existence of quadratic relations between periods of meromorphic flat bundles on complex manifolds with poles along a divisor with normal crossings under the assumption of "goodness". In dimension one, for which goodness is always satisfied, we provide methods to compute the various pairings involved. In an appendix, we give details on the classical results needed for the proofs. V3: Revised version, various proofs simplified in Section 3, exposition improved.
TL;DR: In this article , Cheng's maximal diameter theorem for hypergraphs with positive coarse Ricci curvature was shown to hold for the case where the resolvent of the nonlinear Laplacian of the hypergraph is defined by the resolver.
Abstract: We prove that Cheng's maximal diameter theorem for hypergraphs with positive coarse Ricci curvature. Coarse Ricci curvature on hypergraphs is defined by using the resolvent of the nonlinear Laplacian. As a byproduct of the main theorem, the first non-zero eigenvalue on a hypergraph coincides with the lower bound of the curvature if the hypergraph has the maximal diameter.
TL;DR: In this article , it was shown that there are exactly six left-invariant Lorentzian metrics up to scaling and automorphisms on the 3D Heisenberg group and only one of them is flat.
Abstract: It has been known that there exist exactly three left-invariant Lorentzian metrics up to scaling and automorphisms on the three dimensional Heisenberg group. In this paper, we classify left-invariant Lorentzian metrics on the direct product of three dimensional Heisenberg group and the Euclidean space of dimension $n-3$ with $n \geq 4$, and prove that there exist exactly six such metrics on this Lie group up to scaling and automorphisms. Moreover we show that only one of them is flat, and the other five metrics are Ricci solitons but not Einstein. We also characterize this flat metric as the unique closed orbit, where the equivalence class of each left-invariant metric can be identified with an orbit of a certain group action on some symmetric space.
TL;DR: In this article , the singularities appearing on parallels to tangent developable surfaces of frontal curves are studied and the classification of generic singularities on them for frontal curves in 3 or 4 dimensional Euclidean spaces are given.
Abstract: A tangent developable surface is defined as a ruled developable surface by tangent lines to a space curve and it has singularities at least along the space curve, called the directrix or the edge of regression. The class of tangent developable surfaces is invariant under the parallel deformations. In this paper the notions of tangent developable surfaces and their parallels are naturally generalised for frontal curves in general in Euclidean spaces of arbitrary dimensions. The singularities appearing on parallels to tangent developable surfaces of frontal curves are studied and the classification of generic singularities on them for frontal curves in 3 or 4 dimensional Euclidean spaces are given.
TL;DR: In this paper , various irreducibilities for Markov processes related to topologies and excessive measures are discussed and their relations are presented, and it is shown that, while the fine-irreducibility is sufficient for the symmetric measure (and stationary distribution) to be unique if exists, it is almost necessary.
Abstract: In this paper various irreducibilities for Markov processes related to topologies and excessive measures are discussed and their relations are presented. We shall mainly prove that, while the fine irreducibility is sufficient for the symmetric measure (and stationary distribution) to be unique if exists, it is almost necessary, namely $X$ is $m$-irreducible if $m$ is the unique symmetric measure for $X$.
TL;DR: In this article , the existence of transfers on a generalization of Milnor K-theory called Milnor-Witt Ktheory was studied and a new proof of the fact that it has geometric transfers was given.
Abstract: We study the existence of transfers on a generalization of Milnor K-theory called Milnor-Witt K-theory. We give a new proof of the fact that Milnor-Witt K-theory has geometric transfers. Moreover, we explain how our proof yields a simplification of Morel's conjecture about Bass-Tate-Kato transfers on contracted homotopy sheaves in the context of motivic homotopy theory.
TL;DR: In this paper , it is shown that the functions associated with this coordinate system produce new invariants on cross cap singular points, and using them, they characterize the possible symmetries on cross caps.
Abstract: It is well-known that cross caps on surfaces in the Euclidean 3-space can be expressed in Bruce-West's normal form, which is a special local coordinate system centered at the singular point. In this paper, we show a certain kind of uniqueness of such a coordinate system. In particular, the functions associated with this coordinate system produce new invariants on cross cap singular points. Using them, we characterize the possible symmetries on cross caps.
TL;DR: In this paper , the authors give a purely cubical argument for the localization theorem for the cubical version of higher Chow groups, and prove that the theorem holds for the higher Chow group.
Abstract: We give a purely cubical argument for the localization theorem for the cubical version of higher Chow groups.
TL;DR: In this paper , the Hartree-Fock Euler-Lagrange equation was shown to be a union of a finite number of connected real-analytic spaces, which is a basis for the study of approximation methods to solve the equation.
Abstract: The Hartree-Fock equation which is the Euler-Lagrange equation corresponding to the Hartree-Fock energy functional is used in many-electron problems. Since the Hartree-Fock equation is a system of nonlinear eigenvalue problems, the study of structures of sets of all solutions needs new methods different from that for the set of eigenfunctions of linear operators. In this paper we prove that the sets of all solutions to the Hartree-Fock equation associated with critical values of the Hartree-Fock energy functional less than the first energy threshold are unions of a finite number of compact connected real-analytic spaces. The result would also be a basis for the study of approximation methods to solve the equation.