4. Mathematics
  5. Optimization and Control

Young-Heon Kim

Mathematics – Optimization and Control

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A Generalization of Caffarelli's Contraction Theorem via (reverse) Heat Flow

Mathematics – Analysis of PDEs
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Continuity and injectivity of optimal maps for non-negatively cross-curved costs

Mathematics – Analysis of PDEs
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Continuity, curvature, and the general covariance of optimal transportation

Mathematics – Differential Geometry
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Counterexamples to continuity of optimal transportation on positively curved Riemannian manifolds

Mathematics – Differential Geometry
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Hölder continuity and injectivity of optimal maps

Mathematics – Analysis of PDEs
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