Minimal hypersurfaces and bordism of positive scalar curvature metrics

DOI10.1007/s00208-017-1629-9zbMath1393.53048arXiv1609.09142OpenAlexW2524267609MaRDI QIDQ1751024

Boris Botvinnik, Demetre Kazaras

Publication date: 23 May 2018

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.09142

zbMATH Keywords

bordismpositive scalar curvaturemanifolds with boundarystable minimal hypersurfaces

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Elliptic equations on manifolds, general theory (58J05) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Surgery and handlebodies (57R65)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A strict maximum principle for area minimizing hypersurfaces
• The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature
• Optimal regularity for codimension one minimal surfaces with a free boundary
• On the structure of manifolds with positive scalar curvature
• Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary
• The Yamabe problem on manifolds with boundary
• Curvature estimates for minimal hypersurfaces
• A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture
• Addendum: Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature
• Elliptic partial differential equations of second order
• Manifolds of positive scalar curvature and conformal cobordism theory
• Construction of embedded area-minimizing surfaces via a topological type induction scheme
• Generic regularity of homologically area minimizing hypersurfaces in eight dimensional manifolds
• Curvature estimates for stable free boundary minimal hypersurfaces
• Compactness of the space of embedded minimal surfaces with free boundary in three-manifolds with nonnegative Ricci curvature and convex boundary
• On the first variation of a varifold
• Area minimizing hypersurfaces with isolated singularities.
• Regularity of stable minimal hypersurfaces
• Conformal deformation of a Riemannian metric to a constant scalar curvature metric with constant mean curvature on the boundary
• Critical points of the total scalar curvature plus total mean curvature functional
• Metrics of Positive Scalar Curvature on Spherical Space Forms
• Riemannian Geometry
• A General Existence Theorem for Embedded Minimal Surfaces with Free Boundary

This page was built for publication: Minimal hypersurfaces and bordism of positive scalar curvature metrics