The cost functions considered are c(x,y)=h(x -y), where h∈C^2(R^n) is homogeneous of degree p≥2 with a positive definite Hessian in the unit sphere. We study multivalued monotone maps with respect to that cost and establish that they are single-valued almost everywhere. Further consequences are then deduced.
Gutiérrez, C.E., Montanari, A. (2025). Fine properties of monotone maps arising in optimal transport for non-quadratic costs. ANALYSIS AND GEOMETRY IN METRIC SPACES, 13(1), 1-14 [10.1515/agms-2025-0023].
Fine properties of monotone maps arising in optimal transport for non-quadratic costs
Montanari, Annamaria
2025
Abstract
The cost functions considered are c(x,y)=h(x -y), where h∈C^2(R^n) is homogeneous of degree p≥2 with a positive definite Hessian in the unit sphere. We study multivalued monotone maps with respect to that cost and establish that they are single-valued almost everywhere. Further consequences are then deduced.File in questo prodotto:
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