A refinement of Günther's candle inequality

Benoit Kloeckner (1) , Greg Kuperberg (2)

1 IF - Institut Fourier
2 MATH - UC Davis - Department of Mathematics [Univ California Davis]

We analyze an upper bound on the curvature of a Riemannian manifold, using "root-Ricci" curvature, which is in between a sectional curvature bound and a Ricci curvature bound. (A special case of root-Ricci curvature was previously discovered by Osserman and Sarnak for a different but related purpose.) We prove that our root-Ricci bound implies Günther's inequality on the candle function of a manifold, thus bringing that inequality closer in form to the complementary inequality due to Bishop.

Mots clés: Gunther-Bishop Theorem; Riemannian manifold; Ricci curvature; candle function; volume bounds; curvature bounds

Domaines: Géométrie différentielle [math.DG]

Benoit Kloeckner, Greg Kuperberg. A refinement of Günther's candle inequality. Asian Journal of Mathematics, 2015, 19, pp.121-134. ⟨hal-00688285v3⟩