arXiv Open Access 2017

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

S. Brendle K. Choi

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Abstrak

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 $κ$-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.

Topik & Kata Kunci

math.DG math.AP

Penulis (2)

S. Brendle

K. Choi

Format Sitasi

APA MLA BibTeX

Brendle, S., Choi, K. (2017). Uniqueness of convex ancient solutions to mean curvature flow in $\mathbb{R}^3$. https://arxiv.org/abs/1711.00823

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Informasi Jurnal

Tahun Terbit: 2017
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓