Lower bounds for contraction constants of non-zero degree mappings onto the sphere

✍ Scribed by Eleonora Ciriza; Marcelo Llarull

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 61 KB
• Volume: 14
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(01)00036-5

✦ Synopsis

This paper studies contraction constants of non-zero degree mappings from compact spin Riemannian manifolds onto the standard Riemannian sphere. Assuming uniform lower bound for the scalar curvature, we find a sharp lower bound for the dilation constants in terms of the dimension of the sphere. In the best case, we prove rigidity.