The Logarithmic Capacitary Minkowski Problem for Polytopes

The logarithmic capacitary Minkowski problem asks for necessary and sufficient conditions on a finite Borel measure on the unit sphere so that it is the logarithmic capacitary measure of a convex body. This article completely solves the case of discrete measures whose support sets are in general pos...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 38; no. 2; pp. 406 - 418
Main Authors Xiong, Ge, Xiong, Jia Wei
Format Journal Article
LanguageEnglish
Published Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.02.2022
Springer Nature B.V
Subjects
Differential geometry
Mathematics
Mathematics and Statistics
Polytopes
Position measurement
52A20
Minkowski problem
31B15
polytope
capacity
general position
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Summary:The logarithmic capacitary Minkowski problem asks for necessary and sufficient conditions on a finite Borel measure on the unit sphere so that it is the logarithmic capacitary measure of a convex body. This article completely solves the case of discrete measures whose support sets are in general position.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-022-1110-x