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The isoperimetric inequality in steady Ricci solitons

2019/12/11 by Yuqiao Li, Li, Yuqiao
Mathematics · #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1912.05250

openalex publication_date 2019/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the isoperimetric inequality is satisfied in the cigar steady soliton and in the Bryant steady soliton. Since both of them are Riemannian manifolds with warped product metric, we utilize the result of Guan-Li-Wang to get our conclusion. For the sake of the soliton structure, we believe that the geometric restrictions for manifolds in which the isoperimetric inequality holds are naturally satisfied for steady Ricci solitons.

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