Minimal hypersurfaces with bounded index
| Autor: | Otis Chodosh, Daniel Ketover, Davi Maximo |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Sequence Structural theorem General Mathematics 010102 general mathematics Degenerate energy levels Dimension (graph theory) Geometric Topology (math.GT) Riemannian manifold 01 natural sciences Mathematics - Geometric Topology Compact space Differential Geometry (math.DG) Bounded function 0103 physical sciences FOS: Mathematics Uniform boundedness 010307 mathematical physics Mathematics::Differential Geometry 0101 mathematics Mathematics |
| DOI: | 10.48550/arxiv.1509.06724 |
| Popis: | We prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index (and volume if the ambient dimension is greater than three) in a Riemannian manifold of dimension at most seven, can degenerate. Loosely speaking, our results show that embedded minimal hypersurfaces with bounded index behave qualitatively like embedded stable minimal hypersurfaces, up to controlled errors. Several compactness/finiteness theorems follows our local picture. Comment: Final version |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|