{"title":"各向异性流、熵和-闵科夫斯基问题","authors":"Károly J. Böröczky, Pengfei Guan","doi":"10.4153/s0008414x23000792","DOIUrl":null,"url":null,"abstract":"<p>We provide a natural simple argument using anistropic flows to prove the existence of weak solutions to Lutwak’s <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231214042727186-0503:S0008414X23000792:S0008414X23000792_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$L^p$</span></span></img></span></span>-Minkowski problem on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231214042727186-0503:S0008414X23000792:S0008414X23000792_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$S^n$</span></span></img></span></span> which were obtained by other methods.</p>","PeriodicalId":501820,"journal":{"name":"Canadian Journal of Mathematics","volume":"83 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Anisotropic flow, entropy, and -Minkowski problem\",\"authors\":\"Károly J. Böröczky, Pengfei Guan\",\"doi\":\"10.4153/s0008414x23000792\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We provide a natural simple argument using anistropic flows to prove the existence of weak solutions to Lutwak’s <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231214042727186-0503:S0008414X23000792:S0008414X23000792_inline2.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$L^p$</span></span></img></span></span>-Minkowski problem on <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231214042727186-0503:S0008414X23000792:S0008414X23000792_inline3.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$S^n$</span></span></img></span></span> which were obtained by other methods.</p>\",\"PeriodicalId\":501820,\"journal\":{\"name\":\"Canadian Journal of Mathematics\",\"volume\":\"83 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Canadian Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4153/s0008414x23000792\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4153/s0008414x23000792","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We provide a natural simple argument using anistropic flows to prove the existence of weak solutions to Lutwak’s $L^p$-Minkowski problem on $S^n$ which were obtained by other methods.
$L^p$-Minkowski problem on 
$S^n$ which were obtained by other methods.
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