Alexander Mramor

activity

20172026

most citedLow Entropy and the Mean Curvature Flow with Surgery

5 citations · 8 across the 14 of their papers we have counts for

collaborators

16 papers

math.DG2026

On asymptotically conical curve shortening flows with convex projections

Alexander Mramor

In this work we study the long term behavior of the curve shortening flow of asymptotically conical curves with convex projections in $R^{3}$ .

math.DG2025

An Ancient Stacked Pancake Solution to Mean Curvature Flow

Alexander Mramor, Louis Yudowitz

We construct an embedded ancient solution to the mean curvature flow which is qualitatively given by a ``stack'' of two ancient pancakes joined by a neck. Our solution is closed, n…

math.DG2024

On the long-time limit of the mean curvature flow in closed manifolds

Alexander Mramor, Ao Sun

In this article we show that generally almost regular flows, introduced by Bamler and Kleiner, in closed 3-manifolds will either go extinct in finite time or flow to a collection o…

math.DG2022

Nonplanar ancient curve shortening flows in $R^{3}$ from grim reapers

Theodora Bourni, Alexander Mramor

In this note we construct new nonplanar ancient (in fact, eternal) solutions to the curve shortening flow in $R^{3}$ , built out of translating grim reapers laying in perpend…

math.DG2021★ 1 cited

On self shrinkers of medium entropy in $R^{4}$

Alexander Mramor

In this article we study smooth asymptotically conical self shrinkers in $R^{4}$ with Colding-Minicozzi entropy bounded above by $Λ_{1}$ .

math.DG2020

An unknottedness result for self shrinkers with multiple ends

Alexander Mramor

In this article we prove an unknottedness result for self shrinkers in $R^{3}$ with multiple asymptotically conical ends which bound a handlebody in a natural sense, using t…

math.DG2020★ 1 cited

An unknottedness result for noncompact self shrinkers

Alexander Mramor

In this article we extend an unknottedness theorem for compact self shrinkers to the mean curvature flow to shrinkers with one asymptotically conical end, which conjecturally compr…

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.DG2019

Nonconvex Surfaces which Flow to Round Points

Alexander Mramor, Alec Payne

In this article, we extend Huisken's theorem that convex surfaces flow to round points by mean curvature flow. We construct certain classes of mean convex and non-mean convex hyper…

math.DG2018★ 5 cited

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

Regularity and stability results for the level set flow via the mean curvature flow with surgery

Alexander Mramor

In this article we use the mean curvature flow with surgery to derive regularity estimates for the level set flow going past Brakke regularity in certain special conditions allowin…

math.DG2017★ 1 cited

On the topological rigidity of self shrinkers in $R^{3}$

Alexander Mramor, Shengwen Wang

In this note we show that compact self shrinkers in $R^{3}$ are "topologically standard" in that any genus $g$ compact self shrinker is ambiently isotopic to the standard ge…

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…

math.DG2017

A finiteness theorem via the mean curvature flow with surgery

Alexander Mramor

In this article, we use the recently developed mean curvature flow with surgery for 2 convex hypersurfaces to prove several isotopy existence and finally extrinsic finiteness resul…

On asymptotically conical curve shortening flows with convex projections

An Ancient Stacked Pancake Solution to Mean Curvature Flow

On the long-time limit of the mean curvature flow in closed manifolds

Nonplanar ancient curve shortening flows in R3 from grim reapers

On self shrinkers of medium entropy in R4

An unknottedness result for self shrinkers with multiple ends

An unknottedness result for noncompact self shrinkers

Compactness and finiteness theorems for rotationally symmetric self shrinkers

On the construction of closed nonconvex nonsoliton ancient mean curvature flows

Ancient and Eternal Solutions to Mean Curvature Flow from Minimal Surfaces

Nonconvex Surfaces which Flow to Round Points

Low Entropy and the Mean Curvature Flow with Surgery

Regularity and stability results for the level set flow via the mean curvature flow with surgery

On the topological rigidity of self shrinkers in R3

Entropy and generic mean curvature flow in curved ambient spaces

A finiteness theorem via the mean curvature flow with surgery

Nonplanar ancient curve shortening flows in $R^{3}$ from grim reapers

On self shrinkers of medium entropy in $R^{4}$

On the topological rigidity of self shrinkers in $R^{3}$