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pro vyhledávání: '"Tsuji Hiroshi"'
Autor:
Tsuji Hiroshi
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 9, Iss 1, Pp 219-253 (2021)
In this paper, we consider a dilation type inequality on a weighted Riemannian manifold, which is classically known as Borell’s lemma in high-dimensional convex geometry. We investigate the dilation type inequality as an isoperimetric type inequali
Externí odkaz:
https://doaj.org/article/cc180952fc8a4576b99da903b6abbe14
Autor:
Nakamura, Shohei, Tsuji, Hiroshi
Motivated by the barycenter problem in optimal transportation theory, Kolesnikov--Werner recently extended the notion of the Legendre duality relation for two functions to the case for multiple functions. We further generalize the duality relation an
Externí odkaz:
http://arxiv.org/abs/2409.13611
Relying substantially on work of Garg, Gurvits, Oliveira and Wigderson, it is shown that geometric Brascamp--Lieb data are, in a certain sense, ubiquitous. This addresses a question raised by Bennett and Tao in their recent work on the adjoint Brasca
Externí odkaz:
http://arxiv.org/abs/2407.21440
We reveal the relation between the Legendre transform of convex functions and heat flow evolution, and how it applies to the functional Blaschke-Santalo inequality. We also describe local maximizers in this inequality.
Externí odkaz:
http://arxiv.org/abs/2403.15357
Autor:
Nakamura, Shohei, Tsuji, Hiroshi
We prove that the functional volume product for even functions is monotone increasing along the Fokker--Planck heat flow. This in particular yields a new proof of the functional Blaschke--Santal\'{o} inequality by K. Ball and also Artstein-Avidan--Kl
Externí odkaz:
http://arxiv.org/abs/2401.00427
Autor:
Tsuji, Hiroshi
We discuss an analytic form of the dilation inequality for symmetric convex sets in Euclidean spaces, which is a counterpart of analytic aspects of Cheeger's isoperimetric inequality. We show that the dilation inequality for symmetric convex sets is
Externí odkaz:
http://arxiv.org/abs/2305.07268
Autor:
Nakamura, Shohei, Tsuji, Hiroshi
We explore an interplay between an analysis of diffusion flows such as Ornstein--Uhlenbeck flow and Fokker--Planck flow and inequalities from convex geometry regarding the volume product. More precisely, we introduce new types of hypercontractivity f
Externí odkaz:
http://arxiv.org/abs/2212.02866
Stability of hypercontractivity, the logarithmic Sobolev inequality, and Talagrand's cost inequality
We provide deficit estimates for Nelson's hypercontractivity inequality, the logarithmic Sobolev inequality, and Talagrand's transportation cost inequality under the restriction that the inputs are semi-log-subharmonic, semi-log-convex, or semi-log-c
Externí odkaz:
http://arxiv.org/abs/2201.12478
Autor:
Tsuji, Hiroshi
In this paper, we consider a dilation type inequality on a weighted Riemannian manifold, which is classically known as Borell's lemma in high-dimensional convex geometry. We investigate the dilation type inequality as an isoperimetric type inequality
Externí odkaz:
http://arxiv.org/abs/2104.04705
Autor:
Tsuji, Hiroshi
In this paper, we study the symmetrized Talagrand inequality that was proved by Fathi and has a connection with the Blaschke-Santal\'{o} inequality in convex geometry. As corollaries of our results, we have several refined functional inequalities und
Externí odkaz:
http://arxiv.org/abs/2004.12295