![]() Firstly, the support of the associated measures must be relatively c-convex and secondly, the so-called MTW tensor must be non-negative definite. From the work of Ma, Trudinger, Wang, and Loeper, two assumptions must be made in order to establish $C^2$-regularity. The solutions of optimal transport problems are induced from solutions to associated Monge-Ampere equations. Speaker: Gabriel Khan (University of Michigan)Ībstract: In this talk, we consider the regularity theory of optimal transport and relate it to the curvature of certain Kahler metrics. Title: Complex geometry and optimal transport Some open problems and conjectures are also presented.Add to Calendar 14:30:00 15:30:00 Differential Geometry Seminar - Gabriel Khan Related to these problems and describe two new approaches - one conventionalĪnd the other computer-assisted - to make progress on the illumination We also include some of our recent results Special care is taken to include the recent advances that are notĬovered by the existing surveys. Geometry, computational geometry and geometric analysis motivated by thisĬonjecture. In this paper, we survey the activity in the areas of discrete ![]() ![]() Longstanding open problems in discrete geometry, namely, the IlluminationĬonjecture. They are inįact two sides of the same coin and give rise to one of the important Smaller positive homothetic copies appear to be quite different. Khan Download PDF Abstract: At a first glance, the problem of illuminating the boundary of a convex bodyīy external light sources and the problem of covering a convex body by its Download a PDF of the paper titled The geometry of homothetic covering and illumination, by Karoly Bezdek and Muhammad A.
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