{"title":"关于 σκ-Nirenberg 问题","authors":"YanYan Li, Luc Nguyen, Bo Wang","doi":"10.1353/ajm.2024.a917542","DOIUrl":null,"url":null,"abstract":"<p><p>abstract:</p><p>We consider the problem of prescribing the $\\sigma_k$-curvature on the standard sphere $\\Bbb{S}^n$ with $n\\geq 3$. We prove existence and compactness theorems when $k\\geq n/2$. This extends an earlier result of Chang, Han, and Yang for $n=4$ and $k=2$.</p></p>","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the σκ-Nirenberg problem\",\"authors\":\"YanYan Li, Luc Nguyen, Bo Wang\",\"doi\":\"10.1353/ajm.2024.a917542\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>abstract:</p><p>We consider the problem of prescribing the $\\\\sigma_k$-curvature on the standard sphere $\\\\Bbb{S}^n$ with $n\\\\geq 3$. We prove existence and compactness theorems when $k\\\\geq n/2$. This extends an earlier result of Chang, Han, and Yang for $n=4$ and $k=2$.</p></p>\",\"PeriodicalId\":7453,\"journal\":{\"name\":\"American Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-01-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"American Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1353/ajm.2024.a917542\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1353/ajm.2024.a917542","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We consider the problem of prescribing the $\sigma_k$-curvature on the standard sphere $\Bbb{S}^n$ with $n\geq 3$. We prove existence and compactness theorems when $k\geq n/2$. This extends an earlier result of Chang, Han, and Yang for $n=4$ and $k=2$.
期刊介绍:
The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.