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Singular set and curvature blow-up rate of the level set flow

  • Siao-Hao Guo EMAIL logo

Abstract

Under certain conditions such as the 2-convexity, a singularity of the level set flow is of type I (in the sense that the rate of curvature blow-up is constrained before and after the singular time) if and only if the flow shrinks to either a round point or a C 1 curve near that singular point. Analytically speaking, the arrival time is C 2 near a critical point if and only if it satisfies a Łojasiewicz inequality near the point.

Funding statement: The research was partially supported by the grant 109-2115-M-002-018-MY3 of National Science and Technology Council of Taiwan.

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Received: 2023-02-04
Revised: 2023-10-11
Published Online: 2023-11-20
Published in Print: 2024-02-01

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