As on arXiv
Abstract
For a convex mean curvature flow in , the corresponding arrival time function solves a degenerate elliptic equation that becomes singular at extinction. We prove that it is for any in the plane, with a logarithmic modulus for its twenty-fourth derivatives. We prove that this bound is sharp combining regularity obstruction in our companion paper. We obtain asymptotic expansions of the rescaled flow to any prescribed order, including derivative estimates for the remainder. Combined with the work of Sesum for , this also gives the sharp regularity for convex arrival time functions in higher dimensions.
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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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General regularity obstructions for the arrival time equation
Topics Mean curvature flow · Same authors Yiqi Huang, Jingze Zhu · Shared terms “arrival time”, “time equation”, “time function”
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Arnold-Thom conjecture for the arrival time of surfaces
Topics Mean curvature flow · Same author Jingze Zhu · Shared terms “arrival time”, “time function”, “convex mean”
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The Bounded Diameter Conjecture and Sharp Geometric Estimates for Mean Curvature Flow
Topics Mean curvature flow · Same author Yiqi Huang
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On the rate of convergence of cylindrical singularity in mean curvature flow
Topics Mean curvature flow · Same author Yiqi Huang · Shared terms “rescaled”
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Quantitative long range curvature estimate for mean curvature flow
Topics Mean curvature flow · Same author Jingze Zhu · Shared terms “rescaled”
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Rigidity of ancient ovals in higher dimensional mean curvature flow
Topics Mean curvature flow · Same author Jingze Zhu · Shared terms “Sesum”
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Planarity and convexity for pinched ancient solutions of mean curvature flow
Topics Mean curvature flow · Same author Jingze Zhu
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Spectral quantization for ancient asymptotically cylindrical flows
Topics Mean curvature flow · Same author Jingze Zhu
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In the guidebook
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.