As on arXiv
Abstract
In this article we study the breathers of the mean curvature flow in the Euclidean space. A breather is a solution to the mean curvature flow which repeats itself up to isometry and scaling once in a while. We prove several no breather theorems in the noncompact category, that is, under certain conditions, a breather of the mean curvature flow must be a solitonic solution (self-shrinker, self-expander, or translator).
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Nontrivial breathers for Ricci flow
Topics Boundaries & non-compact · Shared terms “breather”
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Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow
Topics Self-shrinkers & translators, Boundaries & non-compact · Shared terms “self expanders”
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Pseudolocality and uniqueness of Ricci flow on almost Euclidean noncompact manifolds
Topics Boundaries & non-compact · Same authors Liang Cheng, Yongjia Zhang · Shared terms “Euclidean space”
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Poincaré inequality and topological rigidity of translators and self-expanders for the mean curvature flow
Topics Self-shrinkers & translators · Shared terms “self expanders”, “Euclidean space”
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Codimension two mean curvature flow of entire graphs
Topics Self-shrinkers & translators, Boundaries & non-compact · Shared terms “self expanders”
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Self-expanders to the mean curvature flow based on the generalized Lawson-Osserman cone
Topics Self-shrinkers & translators · Shared terms “self expanders”
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The Boundary Term in Huisken's Monotonicity Formula and the Entropy of Translators
Topics Self-shrinkers & translators, Boundaries & non-compact
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Gap theorems for complete self-shrinkers of -mean curvature flows
Topics Self-shrinkers & translators
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.