Parabolic optimal transport equations on manifolds
Parabolic optimal transport equations on manifolds
复制标题
流形上的抛物线最优输运方程
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
M. Warren
中科院分区：
文献类型：
--
作者：
Young;J. Streets;M. Warren
本文研究了一类抛物型方程在紧致黎曼流形上的最优输运问题的解。我们证明了，如果费用满足强MTW条件和远离奇异性，则具有任何适当初始条件的抛物流的解始终存在，并且指数收敛于最优运输问题的解.这样的结果特别适用于球体上的圆度量的距离平方成本和远场反射器天线成本等。
We study a parabolic equation for finding solutions to the optimal transport problem on compact Riemannian manifolds with general cost functions. We show that if the cost satisfies the strong MTW condition and the stay-away singularity property, then the solution to the parabolic flow with any appropriate initial condition exists for all time and it converges exponentially to the solution to the optimal transportation problem. Such results hold in particular, on the sphere for the distance squared cost of the round metric and for the far-field reflector antenna cost, among others.