Level set flow in 3D steady gradient Ricci solitons

2017/09/01 by Chih‐Wei Chen, Chen, Chih-Wei, Kuo-Wei Lee +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1709.00143

openalex publication_date 2017/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (M³, g, f) be a nontrivial 3-dimensional steady gradient Ricci soliton. If the scalar curvature R satisfies c₁r^-b≤ R≤ c₂r^-a for some a∈(0,1], b≥ a, and c₁,c₂>0, then the umbilical ratio of the level sets of f satisfies (2|A|²-H²)/(H²)∈ O(r^6a-(8a2)/(b))∩ O(r^2b-4a).

Citations

• Poisson equation on complete manifolds

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