Positivity of Ma-Trudinger-Wang curvature on Riemannian surfaces

Shi Zhong Du; Qi Rui Li

doi:10.1007/s00526-013-0684-7

Positivity of Ma-Trudinger-Wang curvature on Riemannian surfaces

Shi Zhong Du, Qi Rui Li^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper we consider the optimal transportation on Riemannian surfaces when the cost function is squared distance. The main ingredient is the verification of MTW condition. It is known that MTW condition holds if Gauss curvature is sufficiently close to (Formula presented.) in (Formula presented.) norm. In this paper we give an explicit condition on Gauss curvature such that MTW condition is satisfied.

Original language	English
Pages (from-to)	495-523
Number of pages	29
Journal	Calculus of Variations and Partial Differential Equations
Volume	51
Issue number	3-4
DOIs	https://doi.org/10.1007/s00526-013-0684-7
Publication status	Published - 15 Oct 2014

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abstract = "In this paper we consider the optimal transportation on Riemannian surfaces when the cost function is squared distance. The main ingredient is the verification of MTW condition. It is known that MTW condition holds if Gauss curvature is sufficiently close to (Formula presented.) in (Formula presented.) norm. In this paper we give an explicit condition on Gauss curvature such that MTW condition is satisfied.",

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AU - Li, Qi Rui

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AB - In this paper we consider the optimal transportation on Riemannian surfaces when the cost function is squared distance. The main ingredient is the verification of MTW condition. It is known that MTW condition holds if Gauss curvature is sufficiently close to (Formula presented.) in (Formula presented.) norm. In this paper we give an explicit condition on Gauss curvature such that MTW condition is satisfied.

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Positivity of Ma-Trudinger-Wang curvature on Riemannian surfaces

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