Global pinching theorems of submanifolds in spheres.
Globale Riemannsche Geometrie.
Group Actions and Curvature.
Groupes automatiques et courbure négative (d'après D.B.A. Epstein)
Groups of Isometric Transformations, Basic Connections and Splitting results on Riemannian Manifolds
Growth of a primitive of a differential form
For an exact differential form on a Riemannian manifold to have a primitive bounded by a given function , by Stokes it has to satisfy some weighted isoperimetric inequality. We show the converse up to some constants if has bounded geometry. For a volume form, it suffices to have the inequality ( for every compact domain ). This implies in particular the “well-known” result that if is the universal covering of a compact Riemannian manifold with non-amenable fundamental group, then the volume...
Growth of Jacobi Fields and Divergence of Geodesics.
Growth of weighted volume and some applications
We define cut-off functions in order to allow higher growth for Dirichlet energy. Our results are generalizations of the classical Cheng-Yau’s growth conditions of parabolicity. Finally we give some applications to the function theory of Kähler and quaternionic-Kähler manifolds.
G-Spaces, the Asymptotic Splitting of L2(M) into Irreducibles.