15 citations · 34 across the 5 of their papers we have counts for
5 papers
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…
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…
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…
Holomorphic Extensions of Laplacians and Their Determinants
Young-Heon Kim
The Teichmueller space Teich(S) of a surface S in genus g>1 is a totally real submanifold of the quasifuchsian space QF(S). We show that the determinant of the Laplacian det'(Δ) on…
Holomorphic extensions of determinants of Laplacians
Young-Heon Kim
The Teichmuller space Teich(S) of a surface S in genus g>1 is a real submanifold of the quasifuchsian space QF(S). We show that the determinant of the Laplacian det'(Delta) on Teic…