Generalized Minimizing Movements for the varifold Canham-Helfrich flow

2022/07/07 by Katharina Brazda, Martin Kružík, Brazda, Katharina +3
Mathematics · #49J45 #49Q10 #49Q20 #53C80 #92C10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2207.03426

openalex publication_date 2022/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The gradient flow of the Canham-Helfrich functional is tackled via the Generalized Minimizing Movements approach. We prove the existence of solutions in Wasserstein spaces of varifolds, as well as upper and lower diameter bounds. In the more regular setting of multiply covered C^1,1 surfaces, we provide a Li-Yau-type estimate for the Canham-Helfrich energy and prove the conservation of multiplicity along the evolution.

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