{"title":"关于共形度量的q曲率的正性","authors":"Mingxiang Li , Xingwang Xu","doi":"10.1016/j.jfa.2025.111011","DOIUrl":null,"url":null,"abstract":"<div><div>We mainly show that for a conformal metric <span><math><mi>g</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mfrac><mrow><mn>4</mn></mrow><mrow><mi>n</mi><mo>−</mo><mn>2</mn><mi>m</mi></mrow></mfrac></mrow></msup><mo>|</mo><mi>d</mi><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <span><math><mi>n</mi><mo>≥</mo><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></math></span>, if the <span><math><mn>2</mn><mi>m</mi><mo>−</mo></math></span>order Q-curvature <span><math><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>g</mi></mrow><mrow><mo>(</mo><mn>2</mn><mi>m</mi><mo>)</mo></mrow></msubsup></math></span> is positive and has slow decay barrier near infinity, the lower order Q-curvature <span><math><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>g</mi></mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup></math></span> and <span><math><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>g</mi></mrow><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></msubsup></math></span> are both positive if <em>m</em> is at least two.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 111011"},"PeriodicalIF":1.7000,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On positivity of the Q-curvatures of conformal metrics\",\"authors\":\"Mingxiang Li , Xingwang Xu\",\"doi\":\"10.1016/j.jfa.2025.111011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We mainly show that for a conformal metric <span><math><mi>g</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mfrac><mrow><mn>4</mn></mrow><mrow><mi>n</mi><mo>−</mo><mn>2</mn><mi>m</mi></mrow></mfrac></mrow></msup><mo>|</mo><mi>d</mi><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <span><math><mi>n</mi><mo>≥</mo><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></math></span>, if the <span><math><mn>2</mn><mi>m</mi><mo>−</mo></math></span>order Q-curvature <span><math><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>g</mi></mrow><mrow><mo>(</mo><mn>2</mn><mi>m</mi><mo>)</mo></mrow></msubsup></math></span> is positive and has slow decay barrier near infinity, the lower order Q-curvature <span><math><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>g</mi></mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup></math></span> and <span><math><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>g</mi></mrow><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></msubsup></math></span> are both positive if <em>m</em> is at least two.</div></div>\",\"PeriodicalId\":15750,\"journal\":{\"name\":\"Journal of Functional Analysis\",\"volume\":\"289 8\",\"pages\":\"Article 111011\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-04-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022123625001934\",\"RegionNum\":2,\"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":"Journal of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022123625001934","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On positivity of the Q-curvatures of conformal metrics
We mainly show that for a conformal metric on with , if the order Q-curvature is positive and has slow decay barrier near infinity, the lower order Q-curvature and are both positive if m is at least two.
期刊介绍:
The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published.
Research Areas Include:
• Significant applications of functional analysis, including those to other areas of mathematics
• New developments in functional analysis
• Contributions to important problems in and challenges to functional analysis