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math.FA2024
A generalized Legendre duality relation and Gaussian saturation
Shohei Nakamura, Hiroshi Tsuji
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…
math.FA2024
Duality and Heat flow
Dario Cordero-Erausquin, Nathael Gozlan, Shohei Nakamura +1
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 describ…
math.FA2024★ 2 cited
The functional volume product under heat flow
Shohei Nakamura, Hiroshi Tsuji
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 Bl…