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

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 curve near that singular point. Analytic...

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Published inJournal für die reine und angewandte Mathematik Vol. 2024; no. 807; pp. 1 - 29
Main Author Guo, Siao-Hao
Format Journal Article
LanguageEnglish
Published De Gruyter 01.02.2024
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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 curve near that singular point. Analytically speaking, the arrival time is near a critical point if and only if it satisfies a Łojasiewicz inequality near the point.
AbstractList 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 {C^{1}} curve near that singular point. Analytically speaking, the arrival time is C 2 {C^{2}} near a critical point if and only if it satisfies a Łojasiewicz inequality near the point.
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 curve near that singular point. Analytically speaking, the arrival time is near a critical point if and only if it satisfies a Łojasiewicz inequality near the point.
Author Guo, Siao-Hao
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Snippet 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...
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...
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