As on arXiv
Abstract
We show that a generic levelset 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. 1995), which draws a similar connection between the viscosity solution and Brakke flows.
Comments: 18 pages, 1 figure
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Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Equivalence of weak solution concepts for mean curvature flow
Topics Weak & singular flows · Same authors Anton Ullrich, Tim Laux · Shared terms “viscosity solution”, “distributional solutions”, “level set”
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Generic mean curvature flow with obstacles
Topics Weak & singular flows · Same author Tim Laux · Shared terms “generic level”, “level set”, “Evans”
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Generic Mean Curvature Flow With Rough Weights
Topics Weak & singular flows · Same author Tim Laux · Shared terms “distributional solutions”, “Brakke flows”
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Distributional solutions to mean curvature flow
Topics Weak & singular flows · Same author Tim Laux · Shared terms “distributional solutions”
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Median filter method for mean curvature flow using a random Jacobi algorithm
Topics Mean curvature flow · Same authors Anton Ullrich, Tim Laux · Shared terms “level set”, “addition”
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Minimizing Movements for Anisotropic and Inhomogeneous Mean Curvature Flows
Topics Weak & singular flows · Shared terms “viscosity solution”, “distributional solutions”, “level set”
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De Giorgi varifold solutions to Mean Curvature Flow: a minimizing movements approach
Topics Weak & singular flows · Same author Tim Laux · Shared terms “Sturzenhecker”, “Luckhaus”
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Weak-strong uniqueness for volume-preserving mean curvature flow
Topics Weak & singular flows · Same author Tim Laux · Shared terms “distributional solutions”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 12C.9After Perelman
Singular flows, the Smale conjecture, and Bamler’s theory.
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.