Multiplicity one for min-max theory in compact manifolds with boundary and its applications
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 …
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 …
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 …
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 …
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
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 …
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 …
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 …
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 …
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 …
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 …
mass over time, ie have mass drop. It has long been conjectured that the Brakke flow …