Yau's conjecture for nonlocal minimal surfaces

M Caselli, E Florit-Simon, J Serra - arXiv preprint arXiv:2306.07100, 2023 - arxiv.org
We introduce nonlocal minimal surfaces on closed manifolds and establish a far-reaching
Yau-type result: in every closed, $ n $-dimensional Riemannian manifold we construct …

Nonlocal minimal surfaces: recent developments, applications, and future directions

J Serra - SeMA Journal, 2024 - Springer
Nonlocal minimal surfaces: recent developments, applications, and future directions | SeMA
Journal Skip to main content SpringerLink Account Menu Find a journal Publish with us Track …

Free boundary minimal disks in convex balls

R Haslhofer, D Ketover - arXiv preprint arXiv:2307.01828, 2023 - arxiv.org
In this paper, we prove that every strictly convex 3-ball with nonnegative Ricci-curvature
contains at least 3 embedded free-boundary minimal 2-disks for any generic metric, and at …

The Smale Conjecture and Min-Max Theory

D Ketover, Y Liokumovich - arXiv preprint arXiv:2310.05756, 2023 - arxiv.org
arXiv:2310.05756v1 [math.DG] 9 Oct 2023 Page 1 arXiv:2310.05756v1 [math.DG] 9 Oct 2023
THE SMALE CONJECTURE AND MIN-MAX THEORY DANIEL KETOVER AND YEVGENY …

A strong multiplicity one theorem in min-max theory

ACP Chu, Y Li - arXiv preprint arXiv:2309.07741, 2023 - arxiv.org
It was asked by Marques-Neves [MN17, Section 9] which min-max p-widths of the unit 3-
sphere lie strictly between $2 {\pi}^ 2$ and $8 {\pi} $. We show that the 10th to the 13th …

Rigidity theorems for the area widths of Riemannian manifolds

L Ambrozio, FC Marques, A Neves - arXiv preprint arXiv:2408.14375, 2024 - arxiv.org
The volume spectrum of a compact Riemannian manifold is a sequence of critical values for
the area functional, defined in analogy with the Laplace spectrum by Gromov. In this paper …

Allen-Cahn equation and degenerate minimal hypersurface

J Chen, P Gaspar - arXiv preprint arXiv:2402.18799, 2024 - arxiv.org
arXiv:2402.18799v1 [math.DG] 29 Feb 2024 Page 1 ALLEN-CAHN EQUATION AND
DEGENERATE MINIMAL HYPERSURFACE JINGWEN CHEN1, PEDRO GASPAR2 Abstract. In …

Infinitely Many Half-Volume Constant Mean Curvature Hypersurfaces via Min-Max Theory

L Mazurowski, X Zhou - arXiv preprint arXiv:2405.00595, 2024 - arxiv.org
Let $(M^{n+ 1}, g) $ be a closed Riemannian manifold of dimension $3\le n+ 1\le 5$. We
show that, if the metric $ g $ is generic, then $ M $ contains infinitely many geometrically …

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

A Mramor, A Sun - arXiv preprint arXiv:2412.03475, 2024 - arxiv.org
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 of smooth …

Minimal surfaces with low genus in lens spaces

X Li, T Wang, X Yao - arXiv preprint arXiv:2406.12584, 2024 - arxiv.org
Given a Riemannian $\mathbb {RP}^ 3$ with a bumpy metric or a metric of positive Ricci
curvature, we show that there either exist four distinct minimal real projective planes, or exist …