{"title":"On the prescribed fractional Q-curvatures problem on Sn under pinching conditions","authors":"Zhongwei Tang , Ning Zhou","doi":"10.1016/j.difgeo.2023.102103","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study the prescribed fractional <em>Q</em>-curvatures problem of order 2<em>σ</em> on the <em>n</em>-dimensional standard sphere <span><math><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span>, where <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>, <span><math><mi>σ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mfrac><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></math></span>. By combining critical points at infinity approach with Morse theory we obtain new existence results under suitable pinching conditions.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224523001298","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the prescribed fractional Q-curvatures problem of order 2σ on the n-dimensional standard sphere , where , . By combining critical points at infinity approach with Morse theory we obtain new existence results under suitable pinching conditions.
期刊介绍:
Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.