{"title":"Homological n-systole in (n + 1)-manifolds and bi-Ricci curvature","authors":"Jianchun Chu , Man-Chun Lee , Jintian Zhu","doi":"10.1016/j.aim.2025.110187","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we prove an optimal systolic inequality and the corresponding rigidity in the equality case on closed manifolds with positive bi-Ricci curvature, which generalizes the work of Bray-Brendle-Neves in <span><span>[3]</span></span>. The proof is given in all dimensions based on the method of minimal surfaces under the Generic Regularity Hypothesis, which is known to be true up to dimension ten.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110187"},"PeriodicalIF":1.5000,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0001870825000854","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we prove an optimal systolic inequality and the corresponding rigidity in the equality case on closed manifolds with positive bi-Ricci curvature, which generalizes the work of Bray-Brendle-Neves in [3]. The proof is given in all dimensions based on the method of minimal surfaces under the Generic Regularity Hypothesis, which is known to be true up to dimension ten.
期刊介绍：
Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.
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