most citedTowards the smoothness of optimal maps on Riemannian submersions and Riemannian products (of round spheres in particular)

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math.DG2008★ 14 cited

Towards the smoothness of optimal maps on Riemannian submersions and Riemannian products (of round spheres in particular)

Young-Heon Kim, Robert J. McCann

The key condition A3w of Ma, Trudinger and Wang for regularity of optimal transportation maps is implied by the nonnegativity of a pseudo-Riemannian curvature -- which we call cros…

math.DG2006

Surfaces with boundary: their uniformizations, determinants of Laplacians, and isospectrality

Young-Heon Kim

Let Σbe a compact surface of type (g, n), n > 0, obtained by removing n disjoint disks from a closed surface of genus g. Assuming χ(Σ)<0, we show that on Σ, the set of flat metrics…