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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| Published in | Acta mathematica Sinica. English series Vol. 38; no. 2; pp. 406 - 418 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
01.02.2022
Springer Nature B.V |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Xiong, Jia Wei Xiong, Ge |
| Author_xml | – sequence: 1 givenname: Ge surname: Xiong fullname: Xiong, Ge organization: School of Mathematical Sciences, Tongji University – sequence: 2 givenname: Jia Wei surname: Xiong fullname: Xiong, Jia Wei email: everirst@tongji.edu.cn organization: School of Mathematics and Statistics, Ningbo University |
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| Keywords | 52A20 Minkowski problem 31B15 polytope capacity general position |
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Math.1999138151161171433910.1007/s002220050344 – reference: JerisonDA Minkowski problem for electrostatic capacityActa Math.1996176147139566810.1007/BF02547334 – reference: EvansL CGariepyR FMeasure Theory and Fine Properties of Functions1992Boca RatonCRC Press0804.28001 – reference: GardnerR JGeometric Tomography2006CambridgeCambridge University Press10.1017/CBO9781107341029 – reference: HugDLutwakEYangDOn the Lp Minkowski problem for polytopesDiscrete Comput. Geom.200533699715213229810.1007/s00454-004-1149-8 – reference: CaffarelliL AJerisonDLiebE HOn the case of equality in the Brunn—Minkowski inequality for capacityAdv. Math.1996117193207137164910.1006/aima.1996.0008 – reference: ChenS BLiQ RZhuG XThe logarithmic Minkowski problem for non-symmetric measuresTrans. Amer. Math. Soc.201937126232641389609110.1090/tran/7499 – reference: NirenbergLThe Weyl and Minkowski problems in differential geometry in the largeComm. Pure Appl. 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| Title | The Logarithmic Capacitary Minkowski Problem for Polytopes |
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