Add to ORKGThe entropy functional introduced by Colding and Minicozzi plays a fundamental role in the analysis of mean curvature flow. However, unlike the hypersurface case, relatively little about the entropy is known in the higher-codimension case. In this note, we use measure-theoretical techniques and rigidity results for self-shrinkers to prove a compactness theorem for a family of self-shrinking surfaces with low entropy. Based on this, we prove the existence of entropy minimizers among self-shrinking surfaces and improve some rigidity results.Comment: 14 pages; some typos correcte
In this paper, we generalize Colding-Minicozzi's recent results about codimension-1 self-shrinkers f...
In this paper we study non-compact self-shrinkers first in general codimension and then in codimensi...
We correct some mistakes in “Entropy in A Closed Manifold and Partial Regularity of Mean Curvature F...
The entropy of a hypersurface is given by the supremum over all F-functionals with varying centers a...
In this article we study smooth asymptotically conical self shrinkers in $\mathbb{R}^4$ with Colding...
In this paper, we first use the method of Colding and Minicozzi II [7] to show that K. Smoczyk's cla...
This dissertation concerns the mean curvature flow, a geometric evolution equation for submanifolds,...
Original manuscript July 15, 2009We prove a smooth compactness theorem for the space of embedded sel...
We prove that any sequence {Fn : ∑ → ℝ⁴} of conformally branched compact Lagrangian self-shrinkers t...
We record in this thesis three results concerning entropy and singularities in mean curvature ow (M...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged fro...
In this work, we study the space of complete embedded rotationally symmetric self-shrinking hypersur...
We prove the compactness of self-shrinkers in $\mathbb R^3$ with bounded entropy and fixed genus. As...
The entropy of a hypersurface is a geometric invariant that measures complexity and is invariant und...
Abstract Inspired by the idea of Colding and Minicozzi (Ann Math 182:755–833, 2015), ...
In this paper, we generalize Colding-Minicozzi's recent results about codimension-1 self-shrinkers f...
In this paper we study non-compact self-shrinkers first in general codimension and then in codimensi...
We correct some mistakes in “Entropy in A Closed Manifold and Partial Regularity of Mean Curvature F...
The entropy of a hypersurface is given by the supremum over all F-functionals with varying centers a...
In this article we study smooth asymptotically conical self shrinkers in $\mathbb{R}^4$ with Colding...
In this paper, we first use the method of Colding and Minicozzi II [7] to show that K. Smoczyk's cla...
This dissertation concerns the mean curvature flow, a geometric evolution equation for submanifolds,...
Original manuscript July 15, 2009We prove a smooth compactness theorem for the space of embedded sel...
We prove that any sequence {Fn : ∑ → ℝ⁴} of conformally branched compact Lagrangian self-shrinkers t...
We record in this thesis three results concerning entropy and singularities in mean curvature ow (M...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged fro...
In this work, we study the space of complete embedded rotationally symmetric self-shrinking hypersur...
We prove the compactness of self-shrinkers in $\mathbb R^3$ with bounded entropy and fixed genus. As...
The entropy of a hypersurface is a geometric invariant that measures complexity and is invariant und...
Abstract Inspired by the idea of Colding and Minicozzi (Ann Math 182:755–833, 2015), ...
In this paper, we generalize Colding-Minicozzi's recent results about codimension-1 self-shrinkers f...
In this paper we study non-compact self-shrinkers first in general codimension and then in codimensi...
We correct some mistakes in “Entropy in A Closed Manifold and Partial Regularity of Mean Curvature F...