Alexander Mramor

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20172020

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math.DG2020

Compactness and finiteness theorems for rotationally symmetric self shrinkers

Alexander Mramor

In this note we first show a compactness theorem for rotationally symmetric self shrinkers of entropy less than 2, concluding that there are entropy minimizing self shrinkers diffe…

math.DG2019

On the construction of closed nonconvex nonsoliton ancient mean curvature flows

Theodora Bourni, Mathew Langford, Alexander Mramor

We construct closed, embedded, ancient mean curvature flows in each dimension $n \geq 2$ with the topology of $S^{1} \times S^{n - 1}$ . These examples are not mean convex and not soliton…

math.DG2019

Ancient and Eternal Solutions to Mean Curvature Flow from Minimal Surfaces

Alexander Mramor, Alec Payne

We construct embedded ancient solutions to mean curvature flow related to certain classes of unstable minimal hypersurfaces in $R^{n + 1}$ for $n \geq 2$ . These provide exam…

math.DG2018

Low Entropy and the Mean Curvature Flow with Surgery

Alexander Mramor, Shengwen Wang

In this article, we extend the mean curvature flow with surgery to mean convex hypersurfaces with entropy less than $Λ_{n - 2}$ . In particular, 2-convexity is not assumed. Next we sh…

math.DG2017

Entropy and generic mean curvature flow in curved ambient spaces

Alexander Mramor

In the article, we generalize some recent results of Colding and Minicozzi on generic singularities of mean curvature flow to curved ambient spaces. To do so, we make use of a weig…