25 citations · 29 across the 10 of their papers we have counts for
13 papers
Optimal Transport and Generalized Lagrangian Mean Curvature Flows on Kim-McCann Metrics
Arunima Bhattacharya, Micah Warren, Daniel Weser
We express the mean curvature flow of Lagrangian submanifolds in pseudo-Riemannian manifolds endowed with the Kim-McCann-Warren metric within the framework of generalized mean curv…
Legendrian curve shortening flow in
Gregory Drugan, Weiyong He, Micah W. Warren
Motivated by Legendrian curve shortening flows in , we study the curve shortening flow of figure-eight curves in the plane. We show that, under some symmetry and cu…
Coarse Ricci curvature as a function on
Antonio Ache, Micah Warren
We use the framework used by Bakry and Emery in their work on logarithmic Sobolev inequalities to define a notion of coarse Ricci curvature on smooth metric measure spaces alternat…
Approximating coarse Ricci curvature on submanifolds of Euclidean space
Antonio Ache, Micah Warren
For an embedded submanifold , Belkin and Niyogi showed that one can approximate the Laplacian operator using heat kernels. Using a definition of coarse Ricc…
Ricci Curvature and the Manifold Learning Problem
Antonio G. Ache, Micah W. Warren
Consider a sample of points taken i.i.d from a submanifold of Euclidean space. We show that there is a way to estimate the Ricci curvature of with respect to the induce…
Regularity for the optimal transportation problem with Euclidean distance squared cost on the embedded sphere
Jun Kitagawa, Micah Warren
We give sufficient conditions on initial and target measures supported on the sphere to ensure the solution to the optimal transport problem with the cost is a di…