Translator Disclaimer
May 2018 Density of minimal hypersurfaces for generic metrics
Kei Irie, Fernando Marques, André Neves
Author Affiliations +
Ann. of Math. (2) 187(3): 963-972 (May 2018). DOI: 10.4007/annals.2018.187.3.8

Abstract

For almost all Riemannian metrics (in the $C^\infty$ Baire sense) on a closed manifold $M^{n+1}$, $3\le (n+1)\le 7$, we prove that the union of all closed, smooth, embedded minimal hypersurfaces is dense. This implies there are infinitely many minimal hypersurfaces, thus proving a conjecture of Yau (1982) for generic metrics.

Citation

Download Citation

Kei Irie. Fernando Marques. André Neves. "Density of minimal hypersurfaces for generic metrics." Ann. of Math. (2) 187 (3) 963 - 972, May 2018. https://doi.org/10.4007/annals.2018.187.3.8

Information

Published: May 2018
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2018.187.3.8

Subjects:
Primary: 53C42
Secondary: 49Q05

Keywords: generic metrics , minimal surfaces , Weyl law

Rights: Copyright © 2018 Department of Mathematics, Princeton University

JOURNAL ARTICLE
10 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.187 • No. 3 • May 2018
Back to Top