15 citations · 34 across the 5 of their papers we have counts for
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math.DG2007★ 14 cited
Continuity, curvature, and the general covariance of optimal transportation
Young-Heon Kim, Robert J. McCann
Let M and \bar M be n-dimensional manifolds equipped with suitable Borel probability measures ρand \barρ. Ma, Trudinger & Wang gave sufficient conditions on a transportation cost c…
math.DG2007★ 15 cited
Counterexamples to continuity of optimal transportation on positively curved Riemannian manifolds
Young-Heon Kim
Counterexamples to continuity of optimal transportation on Riemannian manifolds with everywhere positive sectional curvature are provided. These examples show that the condition A3…
math.AP2007★ 5 cited
On the cost-subdifferentials of cost-convex functions
Young-Heon Kim, Robert J. McCann
We are interested in the cost-convex potentials in optimal mass transport theory, and we show by direct and geometric arguments the equivalence between cost-subdifferentials and or…