Variational Principles for Minkowski Type Problems, Discrete Optimal Transport, and Discrete Monge-Ampere Equations
Geometric Topology
2013-02-25 v1 Differential Geometry
Metric Geometry
Abstract
In this paper, we develop several related finite dimensional variational principles for discrete optimal transport (DOT), Minkowski type problems for convex polytopes and discrete Monge-Ampere equation (DMAE). A link between the discrete optimal transport, discrete Monge-Ampere equation and the power diagram in computational geometry is established.
Keywords
Cite
@article{arxiv.1302.5472,
title = {Variational Principles for Minkowski Type Problems, Discrete Optimal Transport, and Discrete Monge-Ampere Equations},
author = {Xianfeng Gu and Feng Luo and Jian Sun and S. -T. Yau},
journal= {arXiv preprint arXiv:1302.5472},
year = {2013}
}
Comments
13 pages, 5 figures