Positivity of Ma-Trudinger-Wang curvature on Riemannian surfaces

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 1 in C 2 norm. In this paper we give an e...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2014-11, Vol.51 (3-4), p.495-523
Main Authors: Du, Shi-Zhong, Li, Qi-Rui
Format: Article
Language:English
Subjects:
Analysis
Calculus
Calculus of variations
Calculus of Variations and Optimal Control
Optimization
Control
Curvature
Ingredients
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Norms
Optimization
Partial differential equations
Systems Theory
Texts
Theoretical
Transportation
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Summary: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 1 in C 2 norm. In this paper we give an explicit condition on Gauss curvature such that MTW condition is satisfied.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-013-0684-7