The Degree Theorem in Higher Rank

By Chris Connell, Benson Farb. 2001

47 citations recorded by the source corpus.

Let N be any closed, Riemannian manifold. In this paper we prove that, for most locally symmetric, nonpositively curved Riemannian manifolds M , and for every continuous map f : N → M , the map f is homotopic to a smooth map with Jacobian bounded by a universal constant, depending (as it must) only on Ricci curvature bounds of N . From this we deduce an extension of Gromov’s Volume Comparison Theorem for negatively curved manifolds to (most) nonpositively curved, locally symmetric manifolds.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aa279e9d919fab3e54d598dd2c2bf9706a0eb1d6

Citations in the corpus

• Degree theorems and Lipschitz simplicial volume for nonpositively curved manifolds of finite volume (2007, unknown): “G T ] 3 0 Ja n 20 09”