Metric Inequalities with Scalar Curvature
| Autor: | Misha Gromov |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
010102 general mathematics Pontryagin class Torus Mathematical proof 01 natural sciences Bounded function 0103 physical sciences Metric (mathematics) Novikov self-consistency principle Mathematics::Differential Geometry 010307 mathematical physics Geometry and Topology 0101 mathematics Analysis Descent (mathematics) Scalar curvature Mathematics |
| Zdroj: | Geometric and Functional Analysis. 28:645-726 |
| ISSN: | 1420-8970 1016-443X |
| DOI: | 10.1007/s00039-018-0453-z |
| Popis: | We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below. In so far as geometry is concerned these inequalities appear as generalisations of the classical bounds on the distances between conjugates points in surfaces with positive sectional curvatures. The techniques of our proofs is based on the Schoen–Yau descent method via minimal hypersurfaces, while the overall logic of our arguments is inspired by and closely related to the torus splitting argument in Novikov’s proof of the topological invariance of the rational Pontryagin classes. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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