Thesis (Ph.D.)--University of Washington, 2014We construct new examples of self-shrinking solutions to mean curvature flow. We first construct an immersed and non-embedded sphere self-shrinker. This result verifies numerical evidence dating back to the 1980's and shows that the rigidity results for constant mean curvature spheres in $\mathbb{R}^3$ and minimal spheres in $S^3$ do not hold for sphere self-shrinkers. Then, in joint work with Stephen Kleene, we construct infinitely many complete, immersed self-shrinkers with rotational symmetry for each of the following topological types: the sphere, the plane, the cylinder, and the torus. We also prove rigidity theorems for self-shrinking solutions to geometric flows. In the setting of mean cu...
In the first part of this thesis, we give a classification of all self-similar solutions to the curv...
Original manuscript July 15, 2009We prove a smooth compactness theorem for the space of embedded sel...
We show that every entire self-shrinking solution on C-1 to the Kahler-Ricci flow must be generated ...
Thesis (Ph.D.)--University of Washington, 2014We construct new examples of self-shrinking solutions ...
Abstract. We present new examples of complete embedded self-similar sur-faces under mean curvature b...
In this paper, we generalize Colding-Minicozzi's recent results about codimension-1 self-shrinkers f...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged fro...
This doctoral dissertation aims to generalize the uniqueness and existence results of self-shrinkers...
In this paper, we first use the method of Colding and Minicozzi II [7] to show that K. Smoczyk's cla...
We show existence of homothetically shrinking solutions of the fractional mean curvature flow, whose...
Partially supported by the Grant No. MTM2017-89677-P, MINECO/AEI/FEDER, UE.In Euclidean space, we in...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged fro...
Let ( ) be a smooth strictly convex solution of det( 2 / ) = exp {(1/2) ∑ =1 ( / ) − } defined on a ...
Author Manuscript August 26, 2009It has long been conjectured that starting at a generic smooth clos...
A self-shrinker characterizes the type I singularity of the mean curvature flow. In this thesis we c...
In the first part of this thesis, we give a classification of all self-similar solutions to the curv...
Original manuscript July 15, 2009We prove a smooth compactness theorem for the space of embedded sel...
We show that every entire self-shrinking solution on C-1 to the Kahler-Ricci flow must be generated ...
Thesis (Ph.D.)--University of Washington, 2014We construct new examples of self-shrinking solutions ...
Abstract. We present new examples of complete embedded self-similar sur-faces under mean curvature b...
In this paper, we generalize Colding-Minicozzi's recent results about codimension-1 self-shrinkers f...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged fro...
This doctoral dissertation aims to generalize the uniqueness and existence results of self-shrinkers...
In this paper, we first use the method of Colding and Minicozzi II [7] to show that K. Smoczyk's cla...
We show existence of homothetically shrinking solutions of the fractional mean curvature flow, whose...
Partially supported by the Grant No. MTM2017-89677-P, MINECO/AEI/FEDER, UE.In Euclidean space, we in...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged fro...
Let ( ) be a smooth strictly convex solution of det( 2 / ) = exp {(1/2) ∑ =1 ( / ) − } defined on a ...
Author Manuscript August 26, 2009It has long been conjectured that starting at a generic smooth clos...
A self-shrinker characterizes the type I singularity of the mean curvature flow. In this thesis we c...
In the first part of this thesis, we give a classification of all self-similar solutions to the curv...
Original manuscript July 15, 2009We prove a smooth compactness theorem for the space of embedded sel...
We show that every entire self-shrinking solution on C-1 to the Kahler-Ricci flow must be generated ...