Inverse mean curvature flow and Ricci-pinched three-manifolds

2023/05/08 by Gerhard Huisken, Huisken, Gerhard, Thomas Koerber +1 · 3 citations
Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2305.04702

openalex publication_date 2023/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (M,g) be a complete, connected, non-compact Riemannian three-manifold with non-negative Ricci curvature satisfying Ric≥ε tr(Ric) g for some ε>0. In this note, we give a new proof based on inverse mean curvature flow that (M,g) is either flat or has non-Euclidean volume growth. In conjunction with results of J. Lott and of M.-C. Lee and P. Topping, this gives an alternative proof of a conjecture of R. Hamilton recently proven by A. Deruelle, F. Schulze, and M. Simon using Ricci flow.

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