Uniqueness of regular shrinkers with two enclosed regions

Uniqueness of regular shrinkers with two enclosed regions

Regular shrinkers describe blow-up limits of a finite-time singularity of the motion by curvature of planar network of curves. This follows from Huisken’s monotonicity formula. In this paper, we show that there is only one regular shrinker with two enclosed regions. This regular shrinker is the Cisg...

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Veröffentlicht in:Geometriae dedicata 2022-04, Vol.216 (2), Article 17
Hauptverfasser: Chang, Jui-En, Lue, Yang-Kai
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
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Zusammenfassung:Regular shrinkers describe blow-up limits of a finite-time singularity of the motion by curvature of planar network of curves. This follows from Huisken’s monotonicity formula. In this paper, we show that there is only one regular shrinker with two enclosed regions. This regular shrinker is the Cisgeminate eye. Moreover, we find some degenerate regular shrinkers with two enclosed regions.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-021-00667-2