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【学术报告】2024年5月8日Dylan Langharst博士来我院举办学术讲座

时间:2024-05-08

报告人:Dylan Langharst法国巴黎左岸数学研究所

邀请人:张宁

报告时间:2024年5月8日(星期三)14:30-16:30

报告地点:东三十一楼119室

报告题目:Weighted Minkowski's Existence Theorem

报告摘要:Minkowski once considered: what are the necessary and sucient conditions for a collection of unit vectors fuig and positive numbers faig to correspond to the convex polytope whose ith face has outer-unit normal ui and surface area ai? His famed existence theorem found there are merely two minor conditions needed to guarantee the existence of a unique, centered polytope with the prescribed properties.For an arbitrary convex body, whose resolution follows from the polytope case, one shows a Borel measure.on the unit sphere is the surface area measure (SK) for a unique centered convex body K.In this talk, we consider replacing volume with some Borel measure that has density. We consider a rich class of Borel measures and solve the following weighted Minkowski's existence theorem: for a nite,even Borel measure on the unit sphere and  an even Borel measure on Rn from the rich class, there exists a symmetric convex body K in Rn such that d(u) = c;KdS;K(u);where c;K is a quantity that depends on  and K and dS;K(u) is the weighted surface area-measure of K with respect to. Examples of measures in the rich class are homogeneous measures (with c;K = 1) and radially decreasing probability measures with continuous densities (e.g. the Gaussian measure). Under certain concavity conditions on the measure, we also obtain uniqueness.Joint with L. Kryvonos.

报告人简介:Dylan Langharst,法国巴黎左岸数学研究所博士后,肯特州立大学博士,师从Artem Zvavitch,主要研究凸几何分析、几何概率等方向,现在Trans of AMS、Proc of LMS、IMRN等优秀期刊上发表文章。


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