Classification of compact ancient solutions to the curve shortening flow

Panagiota Daskalopoulos; Richard Hamilton; Natasa Sesum

doi:10.4310/jdg/1279114297

Classification of compact ancient solutions to the curve shortening flow

Panagiota Daskalopoulos, Richard Hamilton, Natasa Sesum

Research output: Contribution to journal › Article › peer-review

49 Scopus citations

Abstract

We consider an embedded convex compact ancient solution Г_t to the curve shortening flow in ℝ². We prove that Г_t is either a family of contracting circles, which is a type I ancient solution, or a family of evolving Angenent ovals, which is of type II.

Original language	English (US)
Pages (from-to)	455-464
Number of pages	10
Journal	Journal of Differential Geometry
Volume	84
Issue number	3
DOIs	https://doi.org/10.4310/jdg/1279114297
State	Published - 2010
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Geometry and Topology

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title = "Classification of compact ancient solutions to the curve shortening flow",

abstract = "We consider an embedded convex compact ancient solution Гt to the curve shortening flow in ℝ2. We prove that Гt is either a family of contracting circles, which is a type I ancient solution, or a family of evolving Angenent ovals, which is of type II.",

author = "Panagiota Daskalopoulos and Richard Hamilton and Natasa Sesum",

year = "2010",

doi = "10.4310/jdg/1279114297",

language = "English (US)",

volume = "84",

pages = "455--464",

journal = "Journal of Differential Geometry",

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T1 - Classification of compact ancient solutions to the curve shortening flow

AU - Daskalopoulos, Panagiota

AU - Hamilton, Richard

AU - Sesum, Natasa

PY - 2010

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N2 - We consider an embedded convex compact ancient solution Гt to the curve shortening flow in ℝ2. We prove that Гt is either a family of contracting circles, which is a type I ancient solution, or a family of evolving Angenent ovals, which is of type II.

AB - We consider an embedded convex compact ancient solution Гt to the curve shortening flow in ℝ2. We prove that Гt is either a family of contracting circles, which is a type I ancient solution, or a family of evolving Angenent ovals, which is of type II.

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JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

IS - 3

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Classification of compact ancient solutions to the curve shortening flow

Abstract

All Science Journal Classification (ASJC) codes

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