Generic Level Sets in Mean Curvature Flow are BV Solutions

We show that a generic level set of the viscosity solution to mean curvature flow is a distributional solution in the framework of sets of finite perimeter by Luckhaus and Sturzenhecker, which in addition saturates the optimal energy dissipation rate. This extends the fundamental work of Evans and S...

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Bibliographic Details
Published in:The Journal of geometric analysis 2024-12, Vol.34 (12), Article 375
Main Authors: Ullrich, Anton, Laux, Tim
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
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Summary:We show that a generic level set of the viscosity solution to mean curvature flow is a distributional solution in the framework of sets of finite perimeter by Luckhaus and Sturzenhecker, which in addition saturates the optimal energy dissipation rate. This extends the fundamental work of Evans and Spruck (J Geom Anal 5(1):79–116, 1995), which draws a similar connection between the viscosity solution and Brakke flows.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-024-01819-y