Add to ORKGThe entropy of a hypersurface is a geometric invariant that measures complexity and is invariant under rigid motions and dilations. It is given by the supremum over all Gaussian integrals with varying centers and scales. It is monotone under mean curvature flow, thus giving a Lyapunov functional. Therefore, the entropy of the initial hypersurface bounds the entropy at all future singularities. We show here that not only does the round sphere have the lowest entropy of any closed singularity, but there is a gap to the second lowest.National Science Foundation (U.S.) (Grant DMS 11040934)National Science Foundation (U.S.) (Grant DMS 0906233)National Science Foundation (U.S.). Focused Research Group (Grant DMS 0854774)National Science Foundatio...
We record work done by the author joint with John Ross [27] on stable smooth solutions to the gaussi...
On every closed contact manifold there exist contact forms with volume one whose Reeb flows have arb...
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...
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...
The entropy functional introduced by Colding and Minicozzi plays a fundamental role in the analysis ...
We prove the compactness of self-shrinkers in $\mathbb R^3$ with bounded entropy and fixed genus. As...
In this work, we study the space of complete embedded rotationally symmetric self-shrinking hypersur...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged fro...
In this note, we consider the entropy of unit area translation surfaces in the $SL(2, \mathbb R)$ or...
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...
The volume entropy of a compact metric measure space is known to be the exponential growth rate of t...
In 2012, Colding-Ilmanen-Minicozzi-White conjectured that the entropy of any closed surface in R^3 i...
We record work done by the author joint with John Ross [27] on stable smooth solutions to the gaussi...
On every closed contact manifold there exist contact forms with volume one whose Reeb flows have arb...
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...
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...
The entropy functional introduced by Colding and Minicozzi plays a fundamental role in the analysis ...
We prove the compactness of self-shrinkers in $\mathbb R^3$ with bounded entropy and fixed genus. As...
In this work, we study the space of complete embedded rotationally symmetric self-shrinking hypersur...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged fro...
In this note, we consider the entropy of unit area translation surfaces in the $SL(2, \mathbb R)$ or...
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...
The volume entropy of a compact metric measure space is known to be the exponential growth rate of t...
In 2012, Colding-Ilmanen-Minicozzi-White conjectured that the entropy of any closed surface in R^3 i...
We record work done by the author joint with John Ross [27] on stable smooth solutions to the gaussi...
On every closed contact manifold there exist contact forms with volume one whose Reeb flows have arb...
We prove that any sequence {Fn : ∑ → ℝ⁴} of conformally branched compact Lagrangian self-shrinkers t...