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Minimal Hypersurfaces with Arbitrarily Large Area

Published:2019-07-09 Issue:14 Volume:2021 Page:10841-10847
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Chodosh Otis¹,Mantoulidis Christos²

Affiliation:

1. Department of Mathematics, Princeton University, Princeton, NJ 08544, USA and School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA

2. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Abstract

Abstract For $3\leq n\leq 7$, we prove that a bumpy closed Riemannian $n$-manifold contains a sequence of connected embedded closed minimal surfaces with unbounded area.

Funder

National Science Foundation

International Centre for Mathematical Sciences

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/14/10841/38934038/rnz128.pdf

Reference24 articles.

1. Generic finiteness of minimal surfaces with bounded Morse index;Carlotto;Ann. Sc. Norm. Super. Pisa Cl. Sci. (5),2017

2. Minimal hypersurfaces with bounded index;Chodosh;Invent. Math.,2017

3. Minimal surfaces and the Allen–Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates;Chodosh,2018

4. Embedded minimal surfaces without area bounds in 3-manifolds;Colding,2000

5. Comparison between second variation of area and second variation of energy of a minimal surface;Ejiri;Adv. Calc. Var.,2008

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Existence of minimal hypersurfaces with arbitrarily large area and possible obstructions;Journal of Functional Analysis;2024-09

2. Existence of infinitely many minimal hypersurfaces in closed manifolds;Annals of Mathematics;2023-05-01

3. On the existence of minimal hypersurfaces with arbitrarily large area and Morse index;Geometry & Topology;2022-12-13

4. Berger’s Inequality in the Presence of Upper Sectional Curvature Bound;International Mathematics Research Notices;2021-04-13

5. Minimal surfaces and the Allen--Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates;Annals of Mathematics;2020-01-01

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