Volume comparison theorems without Jacobi fields

Dominique Bakry (1) , Zhongmin Qian (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

Using a generalized curvature-dimension inequality and a new approach, we preset a differential inequality for an elliptic second order differential operator acting on distance functions, from which we deduce volume comparison theorems and diameter bounds without the use of the theory of Jacobi fields

Mots clés: Riemannian volume; volume comparison; elliptic operators; invariant measure; curvature-dimension inequality

Domaines: Géométrie différentielle [math.DG]; Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Dominique Bakry, Zhongmin Qian. Volume comparison theorems without Jacobi fields. Conference on Potential Theory, 2005, Bucarest, Romania. p.115-122. ⟨hal-00353652⟩