Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Kitabeppu, Yu"'
Autor:
Kitabeppu, Yu
We prove the Shannon's inequality on non-collapsing $\mathsf{RCD}(0,N)$ spaces. In the proof, we use the characterization of the $\mathsf{EVI}_{0,N}$-gradient flow of the relative entropy and the infinitesimal behavior of the heat kernel. Also we hav
Externí odkaz:
http://arxiv.org/abs/2404.06719
Ambrosio, Honda, and Tewodrose proved that the regular Weyl's law is equivalent to a mild condition related to the infinitesimal behavior of the measure of balls in compact finite dimensional RCD spaces. Though that condition is seemed to always hold
Externí odkaz:
http://arxiv.org/abs/2302.09494
Publikováno v:
Nonlinear Analysis 228 (2023)
We extend the celebrated rigidity of the sharp first spectral gap under $Ric\ge0$ to compact infinitesimally Hilbertian spaces with non-negative (weak, also called synthetic) Ricci curvature and bounded (synthetic) dimension i.e. to so-called compact
Externí odkaz:
http://arxiv.org/abs/2110.05045
Autor:
Kitabeppu, Yu, Matsumoto, Erina
We prove that Cheng maximal diameter theorem for hypergraphs with positive coarse Ricci curvature.
Externí odkaz:
http://arxiv.org/abs/2102.09765
In the present paper, we introduce a concept of Ricci curvature on hypergraphs for a nonlinear Laplacian. We prove that our definition of the Ricci curvature is a generalization of Lin-Lu-Yau coarse Ricci curvature for graphs to hypergraphs. We also
Externí odkaz:
http://arxiv.org/abs/2102.00698
In this paper we discuss three distance functions on the set of convex bodies. In particular we study the convergence of Delzant polytopes, which are fundamental objects in symplectic toric geometry. By using these observations, we derive some conver
Externí odkaz:
http://arxiv.org/abs/2003.02293
Autor:
Kitabeppu, Yu
In this paper, we study regular sets in metric measure spaces with bounded Ricci curvature. We prove that the existence of a point in the regular set of the highest dimension implies the positivity of the measure of such regular set. Also we define t
Externí odkaz:
http://arxiv.org/abs/1708.04309
Autor:
Kitabeppu, Yu
We define a Bishop-type inequality on metric measure spaces with Riemannian curvature-dimension condition. The main result in this short article is that any RCD spaces with the Bishop-type inequalities possess only one regular set in not only the mea
Externí odkaz:
http://arxiv.org/abs/1603.04162
Autor:
Kitabeppu, Yu, Lakzian, Sajjad
Publikováno v:
Analysis and Geometry in Metric Spaces 4, 187 - 215 (2016)
In this paper, we give the characterization of metric measure spaces that satisfy synthetic lower Riemannian Ricci curvature bounds (so called $RCD^*(K,N)$ spaces) with \emph{non-empty} one dimensional regular sets. In particular, we prove that the c
Externí odkaz:
http://arxiv.org/abs/1505.00420
Autor:
Kitabeppu, Yu, Lakzian, Sajjad
Publikováno v:
Canadian Mathematical Bulletin 58, no. 4, 787 - 798 (2015)
In this paper, we generalize the finite generation result of Sormani to non-branching $RCD(0,N)$ geodesic spaces (and in particular, Alexandrov spaces) with full support measures. This is a special case of the Milnor's Conjecture for complete non-com
Externí odkaz:
http://arxiv.org/abs/1405.0897