{"title":"对于 $p \\gt 1$ 和 $\\mathfrak{p} 的静电 $mathfrak{p}$ 容量的 $L_p$ Minkowski 问题\\gqslant n^\\ast$","authors":"Xinbao Lu, Ge Xiong, Jiawei Xiong","doi":"10.4310/ajm.2024.v28.n1.a2","DOIUrl":null,"url":null,"abstract":"The existence and uniqueness of solutions to the $L_p$ Minkowski problem for $\\mathfrak{p}$-capacity for $p \\gt 1$ and $\\mathfrak{p} \\geqslant n$ are proved. For this task, the estimation of $\\mathfrak{p}$−capacitary measure controlled below by the surface area measure is achieved. This work is a sequel to the results $\\href{https://doi.org/10.4310/jdg/1606964418}{[45]}$ for $p \\gt 1$ and $1 \\lt \\mathfrak{p} \\lt n$.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The $L_p$ Minkowski problem for the electrostatic $\\\\mathfrak{p}$-capacity for $p \\\\gt 1$ and $\\\\mathfrak{p} \\\\geqslant n^\\\\ast$\",\"authors\":\"Xinbao Lu, Ge Xiong, Jiawei Xiong\",\"doi\":\"10.4310/ajm.2024.v28.n1.a2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The existence and uniqueness of solutions to the $L_p$ Minkowski problem for $\\\\mathfrak{p}$-capacity for $p \\\\gt 1$ and $\\\\mathfrak{p} \\\\geqslant n$ are proved. For this task, the estimation of $\\\\mathfrak{p}$−capacitary measure controlled below by the surface area measure is achieved. This work is a sequel to the results $\\\\href{https://doi.org/10.4310/jdg/1606964418}{[45]}$ for $p \\\\gt 1$ and $1 \\\\lt \\\\mathfrak{p} \\\\lt n$.\",\"PeriodicalId\":55452,\"journal\":{\"name\":\"Asian Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-08-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asian Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/ajm.2024.v28.n1.a2\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/ajm.2024.v28.n1.a2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The $L_p$ Minkowski problem for the electrostatic $\mathfrak{p}$-capacity for $p \gt 1$ and $\mathfrak{p} \geqslant n^\ast$
The existence and uniqueness of solutions to the $L_p$ Minkowski problem for $\mathfrak{p}$-capacity for $p \gt 1$ and $\mathfrak{p} \geqslant n$ are proved. For this task, the estimation of $\mathfrak{p}$−capacitary measure controlled below by the surface area measure is achieved. This work is a sequel to the results $\href{https://doi.org/10.4310/jdg/1606964418}{[45]}$ for $p \gt 1$ and $1 \lt \mathfrak{p} \lt n$.