Multiplicity one for min–max theory in compact manifolds with boundary and its applications
Name
526_2024_2669_ReferencePDF.pdf
Size
906 KB
Format
Adobe PDF
Checksum (MD5)
f1a97ceec0c4c71027a2691adbf1c79e
Author(s)
Sun, Ao
Wang, Zhichao
Zhou, Xin
Date Issued
March 7, 2024
Journal
Calculus of Variations and Partial Differential Equations
Publisher
Springer Berlin Heidelberg
Citation
Sun, A., Wang, Z. & Zhou, X. Multiplicity one for min–max theory in compact manifolds with boundary and its applications. Calc. Var. 63, 70 (2024).
Version
Author's final manuscript
Abstract
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 approach this, we develop existence and regularity theory for free boundary hypersurface with prescribed mean curvature, which includes the regularity theory for minimizers, compactness theory, and a generic min–max theory with Morse index bounds. As applications, we construct new free boundary minimal hypersurfaces in the unit balls in Euclidean spaces and self-shrinkers of the mean curvature flows with arbitrarily large entropy.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00526-024-02669-w
