A mountain pass theorem for minimal hypersurfaces with fixed boundary
Copyright policy )A mountain pass theorem for minimal hypersurfaces with fixed boundary
In this work, we prove the existence of a third embedded minimal hypersurface spanning a closed submanifold $��$ contained in the boundary of a compact Riemannian manifold with convex boundary, when it is known a priori the existence of two strictly stable minimal hypersurfaces that bound $��$. In order to do so, we develop min-max methods similar to those of De Lellis and Ramic, references in the paper, adapted to the discrete setting of Almgren and Pitts.
- University of Massachusetts System United States
- Universidade Federal do Ceará Brazil
- University of Massachusetts Amherst United States
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Mathematics - Differential Geometry, Riemannian manifold, Variational problems concerning minimal surfaces (problems in two independent variables), Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Global Riemannian geometry, including pinching, minimal hypersurface, min-max theory, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), FOS: Mathematics, discretization of maps, local interpolation, Analysis of PDEs (math.AP)
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Mathematics - Differential Geometry, Riemannian manifold, Variational problems concerning minimal surfaces (problems in two independent variables), Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Global Riemannian geometry, including pinching, minimal hypersurface, min-max theory, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), FOS: Mathematics, discretization of maps, local interpolation, Analysis of PDEs (math.AP)
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