Uniqueness of convex ancient solutions to mean curvature flow in $${\mathbb {R}}^3$$ R 3

Autor:	Kyeongsu Choi, Simon Brendle
Rok vydání:	2019
Předmět:	Mean curvature flow Pure mathematics General Mathematics 010102 general mathematics Dimension (graph theory) Regular polygon Ricci flow 01 natural sciences 0103 physical sciences Mathematics::Differential Geometry 010307 mathematical physics Soliton Uniqueness Sectional curvature 0101 mathematics Convex function Mathematics
Zdroj:	Inventiones mathematicae. 217:35-76
ISSN:	1432-1297 0020-9910
DOI:	10.1007/s00222-019-00859-4
Popis:	A well-known question of Perelman concerns the classification of noncompact ancient solutions to the Ricci flow in dimension 3 which have positive sectional curvature and are $$\kappa $$ -noncollapsed. In this paper, we solve the analogous problem for mean curvature flow in $${\mathbb {R}}^3$$ , and prove that the rotationally symmetric bowl soliton is the only noncompact ancient solution of mean curvature flow in $${\mathbb {R}}^3$$ which is strictly convex and noncollapsed.
Databáze:	OpenAIRE
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