Existence of polarized f-structures on collapsed manifolds with bounded curvature and diameter期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Existence of polarized f-structures on collapsed manifolds with bounded curvature and diameter

Authors:	J Cheeger X Rong

Institution:	(1) Courant Institute of Mathematical Sciences, New York University, 10012 New York, NY, USA;(2) Mathematics Department, University of Chicago, 60637 Chicago, IL, USA

Abstract:	We study the class of collapsed Riemanniann-manifolds with bounded sectional curvature and diameter. Our main result asserts that there is a constant,(n, d)>0, such that if a compactn-manifold has bounded curvature, $\|K_{M^n } \| \leqslant 1$ , bounded diameter, diam (M ⁿ)d and sufficiently small volume, Vol(M ⁿ)(n, d), then it admits a mixed polarized F-structure. As a consequence, inf_g Vol(M ⁿ,g)=0, where the infimum is taken over all metrics with $\|K_{(M^n ,g)} \| \leqslant 1$ . This assertion can be viewed as a weakened version of Gromov's critical volume conjecture.The first author is partially supported by NSF Grant DMS 9303999, and the second author is partially supported by NSF Grant DMS 9204095.

Keywords:
本文献已被 SpringerLink 等数据库收录！