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UID:40778
DTSTAMP:20200121T055537Z
SUMMARY:PAN Analysis seminar: Murat Akman (Essex)
LOCATION:SIBSR1
DESCRIPTION:\nAbstract: \nThe classical Minkowski problem consists in finding a convex polyhedron from data consisting of normals to their faces and their surface areas. In the smooth case, the corresponding problem for convex bodies is to find the convex body given the Gauss curvature of its boundary, as a function of the unit normal. The proof consists of three parts: existence, uniqueness and regularity. In this talk, we study a Minkowski problem for certain measure, called p-capacitary surface area measure, associated to a compact convex set E with nonempty interior and its p-harmonic capacitary function. If μ(E) denotes this measure, then the Minkowski problem we consider in this setting is that; for a given finite Borel positive measure μ on S^{n−1}, find necessary and sufficient conditions for which there exists a convex body E with μ(E) =μ. We will discuss the existence, uniqueness, and regularity of this problem which has a deep connection with the Brunn-Minkowski inequality for p-capacity and Monge-Ampère equation.\n\n\n\nSeminars in this series are organised by Dr Marina Iliopoulou and Dr Mark Roelands.\n\n
DTSTART:20191010T120000Z
DTEND:20191010T130000Z
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