Multiplicity one for min-max theory in compact manifolds with boundary and its applications

A Sun, Z Wang, X Zhou - arXiv preprint arXiv:2011.04136, 2020 - arxiv.org
We prove the multiplicity one theorem for min-max free boundary minimal hypersurfaces in
compact manifolds with boundary of dimension between 3 and 7 for generic metrics. To …

Mean curvature flow with generic low-entropy initial data

O Chodosh, K Choi, C Mantoulidis… - Duke Mathematical …, 2024 - projecteuclid.org
We prove that sufficiently low-entropy closed hypersurfaces can be perturbed so that their
mean curvature flow encounters only spherical and cylindrical singularities. Our theorem …

Topological uniqueness for self-expanders of small entropy

J Bernstein, L Wang - arXiv preprint arXiv:1902.02642, 2019 - arxiv.org
arXiv:1902.02642v2 [math.DG] 30 Mar 2020 Page 1 arXiv:1902.02642v2 [math.DG] 30 Mar
2020 TOPOLOGICAL UNIQUENESS FOR SELF-EXPANDERS OF SMALL ENTROPY JACOB …

Free boundary flow with surgery

R Haslhofer - arXiv preprint arXiv:2306.07714, 2023 - arxiv.org
In this paper, we prove the existence of mean curvature flow with surgery for mean-convex
surfaces with free boundary. To do so, we implement our recent new approach for …

Multiplicity one for min–max theory in compact manifolds with boundary and its applications

A Sun, Z Wang, X Zhou - Calculus of Variations and Partial Differential …, 2024 - Springer
We prove the multiplicity one theorem for min–max free boundary minimal hypersurfaces in
compact manifolds with boundary of dimension between 3 and 7 for generic metrics. To …

Flows with surgery revisited

R Haslhofer - arXiv preprint arXiv:2305.16267, 2023 - arxiv.org
In this paper, we introduce a new method to establish existence of geometric flows with
surgery. In contrast to all prior constructions of flows with surgery in the literature our new …

[HTML][HTML] Precise asymptotics near a generic S1× R3 singularity of mean curvature flow

Z Gang, S Wang - Nonlinear Analysis, 2025 - Elsevier
In the present paper we study a type of generic singularity of mean curvature flow modelled
on the bubble-sheet S 1× R 3, and we derive an asymptotic profile for a neighbourhood of …

An unknottedness result for noncompact self shrinkers

A Mramor - arXiv preprint arXiv:2005.01688, 2020 - arxiv.org
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 …

On self-shrinkers of medium entropy in R4

A Mramor - Geometry & Topology, 2023 - msp.org
Self-shrinkers are basic singularity models for the mean curvature flow, and, in the
noncompact case, nongeneric ones (generic ones being generalized round cylinders Sk. p …

Mass Drop and Multiplicity in Mean Curvature Flow

A Payne - arXiv preprint arXiv:2009.14163, 2020 - arxiv.org
Brakke flow is defined with a variational inequality, which means it may have discontinuous
mass over time, ie have mass drop. It has long been conjectured that the Brakke flow …