Growth tightness of negatively curved manifolds

✍ Scribed by Andrea Sambusetti

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 92 KB
• Volume: 336
• Category: Article
• ISSN: 1631-073X
• DOI: 10.1016/s1631-073x(03)00086-4

✦ Synopsis

We show that any closed negatively curved manifold X is growth tight: this means that its universal covering X has an exponential growth rate ω( X) which is strictly greater than the exponential growth rate ω(X) of any other normal covering X. Moreover, we give an explicit formula which estimates the difference between ω( X) and ω( X) in terms of the systole of X and of some geometric parameters of the base manifold X. Then, we describe some applications to systoles and periodic geodesics.