4 citations · 10 across the 10 of their papers we have counts for
16 papers
-transport with discrete target as a combinatorial matching problem
Mohit Bansil, Jun Kitagawa
In this short note, we show that given a cost function , any coupling of two probability measures where the second is a discrete measure can be associated to a certain bipar…
Optimal transport and the Gauss curvature equation
Nestor Guillen, Jun Kitagawa
In this short note, we consider the problem of prescribing the Gauss curvature and image of the Gauss map for the graph of a function over a domain in Euclidean space. The prescrip…
Quantitative stability in the geometry of semi-discrete optimal transport
Mohit Bansil, Jun Kitagawa
We show quantitative stability results for the geometric "cells" arising in semi-discrete optimal transport problems. Our results show two types of stability, the first is stabilit…
Inverse Iteration for the Monge-Ampère Eigenvalue Problem
Farhan Abedin, Jun Kitagawa
We present an iterative method based on repeatedly inverting the Monge-Ampère operator with Dirichlet boundary condition and prescribed right-hand side on a bounded, convex domain…
A Newton algorithm for semi-discrete optimal transport with storage fees
Mohit Bansil, Jun Kitagawa
We introduce and prove convergence of a damped Newton algorithm to approximate solutions of the semi-discrete optimal transport problem with storage fees, corresponding to a proble…
An optimal transport problem with storage fees
Mohit Bansil, Jun Kitagawa
We introduce and investigate properties of a variant of the semi-discrete optimal transport problem. In this problem, one is given an absolutely continuous source measure and cost…
Exponential Convergence of Parabolic Optimal Transport on Bounded Domains
Farhan Abedin, Jun Kitagawa
We study the asymptotic behavior of solutions to the second boundary value problem for a parabolic PDE of Monge-Ampère type arising from optimal mass transport. Our main result is…
Estimates for Dirichlet-to-Neumann maps as integro-differential operators
Nestor Guillen, Jun Kitagawa, Russell W. Schwab
Some linear integro-differential operators have old and classical representations as the Dirichlet-to-Neumann operators for linear elliptic equations, such as the 1/2-Laplacian or…
Free discontinuities in optimal transport
Jun Kitagawa, Robert McCann
We prove a nonsmooth implicit function theorem applicable to the zero set of the difference of convex functions. This theorem is explicit and global: it gives a formula representin…
Pointwise estimates and regularity in geometric optics and other Generated Jacobian Equations
Nestor Guillen, Jun Kitagawa
The study of reflector surfaces in geometric optics necessitates the analysis of certain nonlinear equations of Monge-Ampère type known as generated Jacobian equations. These equat…
Prohibiting isolated singularities in optimal transport
Young-Heon Kim, Jun Kitagawa
We give natural topological conditions on the support of the target measure under which solutions to the optimal transport problem with cost function satisfying the (weak) Ma, Trud…
The multi-marginal optimal partial transport problem
Jun Kitagawa, Brendan Pass
We introduce and study a multi-marginal optimal partial transport problem. Under a natural and sharp condition on the dominating marginals, we establish uniqueness of the optimal p…
The local geometry of maps with c-convex potentials
Nestor Guillen, Jun Kitagawa
We identify a condition for regularity of optimal transport maps that requires only three derivatives of the cost function, for measures given by densities that are only bounded ab…
On the degeneracy of optimal transportation
Young-Heon Kim, Jun Kitagawa
We extend a dimensional upper bound on how much an optimal transport map can degenerate for the quadratic transportation cost, originally due to Caffarelli, to cost functions that…
An iterative scheme for solving the optimal transportation problem
Jun Kitagawa
We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Addition…
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…