Measure Concentration and the Topology of Positively-Curved Riemannian Manifolds

Autor:	Memarian, Yashar
Rok vydání:	2014
Předmět:	Mathematics - Metric Geometry Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	In this paper, I shall demonstrate that sufficiently high-dimensional closed positively-curved Riemannian manifolds are either diffeomorphic to a spherical space form, or isometric to a locally compact rank one symmetric space. This surprising classification of positively-curved Riemannian manifolds results from combining the concentration of measures of Grassmanians with Brendle-Schoen pointwise (weakly)- 1/4-pinching Theorem. A direct corollary of the main result within this paper is the answering of the long standing Hopf Conjecture in sufficiently high dimensions. Comment: This paper has been withdrawn. There is a substantial mistake in section 5 of the paper
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1402.4947 Zobrazit plný text záznamu View this record from Arxiv