{"title":"Integral Ricci curvature bounds for possibly collapsed spaces with Ricci curvature bounded from below","authors":"Michael Smith","doi":"10.1016/j.difgeo.2024.102214","DOIUrl":null,"url":null,"abstract":"<div><div>Assuming a lower bound on the Ricci curvature of a complete Riemannian manifold, for <span><math><mi>q</mi><mo><</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span> we show the existence of bounds on the local <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span> norm of the Ricci curvature that depend only on the dimension and which improve with volume collapse.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102214"},"PeriodicalIF":0.6000,"publicationDate":"2024-11-21","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/S0926224524001074","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
Assuming a lower bound on the Ricci curvature of a complete Riemannian manifold, for we show the existence of bounds on the local norm of the Ricci curvature that depend only on the dimension and which improve with volume collapse.
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.
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