Stability results for nonlocal geometric evolutions and limit cases for\n fractional mean curvature flows

2020/03/04 by Annalisa Cesaroni, Cesaroni, Annalisa, Lucia De Luca +5 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2003.02248

openalex publication_date 2020/03/04 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We introduce a notion of uniform convergence for local and nonlocal\ncurvatures. Then, we propose an abstract method to prove the convergence of the\ncorresponding geometric flows, within the level set formulation. We apply such\na general theory to characterize the limits of s-fractional mean curvature\nflows as s\→ 0⁺ and s\→ 1^-. In analogy with the s-fractional mean\ncurvature flows, we introduce the notion of s-Riesz curvature flows and\ncharacterize its limit as s\→ 0^-. Eventually, we discuss the limit behavior\nas r\→ 0⁺ of the flow generated by a regularization of the r-Minkowski\ncontent.\n

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