Gromov hyperbolic spaces and the sharp isoperimetric constant

• 成果类型: Article
• 署名作者: Wenger, Stefan
• 署名单位: New York University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0084-8
• 发表日期: 2008
• 页码: 227-255
• 关键词: quasi-isometry invariants

摘要

In this article we exhibit the largest constant in a quadratic isoperimetric inequality which ensures that a geodesic metric space is Gromov hyperbolic. As a particular consequence we obtain that Euclidean space is a borderline case for Gromov hyperbolicity in terms of the isoperimetric function. We prove similar results for the linear filling radius inequality. Our results strengthen and generalize theorems of Gromov, Papasoglu and others.