Add to ORKGThesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged from PDF version of thesis.Includes bibliographical references (pages 67-69).In this thesis, we will introduce a notion of index of shrinkers of the mean curvature flow. We will then prove a gap theorem for the index of rotationally symmetric immersed shrinkers in R3, namely, that such shrinkers have index at least 3, unless they are one of the stable ones: the sphere, the cylinder, or the plane. We also provide a generalization of the result to higher dimensions.by Zihan Hans Liu.Ph. D
This dissertation concerns the mean curvature flow, a geometric evolution equation for submanifolds,...
In this article we study smooth asymptotically conical self shrinkers in $\mathbb{R}^4$ with Colding...
Abstract. We present new examples of complete embedded self-similar sur-faces under mean curvature b...
Thesis (Ph.D.)--University of Washington, 2014We construct new examples of self-shrinking solutions ...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged fro...
In this paper, we generalize Colding-Minicozzi's recent results about codimension-1 self-shrinkers f...
We study the Morse index of self-shrinkers for the mean curvature flow and, more generally, of f-min...
In this paper, we first use the method of Colding and Minicozzi II [7] to show that K. Smoczyk's cla...
This doctoral dissertation aims to generalize the uniqueness and existence results of self-shrinkers...
In this paper we study non-compact self-shrinkers first in general codimension and then in codimensi...
Original manuscript July 15, 2009We prove a smooth compactness theorem for the space of embedded sel...
Let ( ) be a smooth strictly convex solution of det( 2 / ) = exp {(1/2) ∑ =1 ( / ) − } defined on a ...
The entropy of a hypersurface is given by the supremum over all F-functionals with varying centers a...
We show, for mean curvature flows in Euclidean space, that if one of the tangent flows at a given sp...
We investigate self-similar solutions to the inverse mean curvature flow in Euclidean space. General...
This dissertation concerns the mean curvature flow, a geometric evolution equation for submanifolds,...
In this article we study smooth asymptotically conical self shrinkers in $\mathbb{R}^4$ with Colding...
Abstract. We present new examples of complete embedded self-similar sur-faces under mean curvature b...
Thesis (Ph.D.)--University of Washington, 2014We construct new examples of self-shrinking solutions ...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged fro...
In this paper, we generalize Colding-Minicozzi's recent results about codimension-1 self-shrinkers f...
We study the Morse index of self-shrinkers for the mean curvature flow and, more generally, of f-min...
In this paper, we first use the method of Colding and Minicozzi II [7] to show that K. Smoczyk's cla...
This doctoral dissertation aims to generalize the uniqueness and existence results of self-shrinkers...
In this paper we study non-compact self-shrinkers first in general codimension and then in codimensi...
Original manuscript July 15, 2009We prove a smooth compactness theorem for the space of embedded sel...
Let ( ) be a smooth strictly convex solution of det( 2 / ) = exp {(1/2) ∑ =1 ( / ) − } defined on a ...
The entropy of a hypersurface is given by the supremum over all F-functionals with varying centers a...
We show, for mean curvature flows in Euclidean space, that if one of the tangent flows at a given sp...
We investigate self-similar solutions to the inverse mean curvature flow in Euclidean space. General...
This dissertation concerns the mean curvature flow, a geometric evolution equation for submanifolds,...
In this article we study smooth asymptotically conical self shrinkers in $\mathbb{R}^4$ with Colding...
Abstract. We present new examples of complete embedded self-similar sur-faces under mean curvature b...