We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Multiplicity one for min–max theory in compact manifolds with boundary and its applications.
- Authors
Sun, Ao; Wang, Zhichao; Zhou, Xin
- 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.
- Subjects
UNIT ball (Mathematics); MULTIPLICITY (Mathematics); MORSE theory; HYPERSURFACES; CURVATURE
- Publication
Calculus of Variations & Partial Differential Equations, 2024, Vol 63, Issue 3, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-024-02669-w