Curvature estimates for submanifolds immersed into horoballs and horocylinders
Differential Geometry
2015-06-11 v2
Abstract
We prove mean curvature estimates and a Jorge-Koutroufiotis type theorem for submanifolds confined into either a horocylinder of N X L or a horoball of N, where N is a Cartan-Hadamard manifold with pinched curvature. Thus, these submanifolds behave in many respects like submanifolds immersed into compact balls and into cylinders over compact balls. The proofs rely on the Hessian comparison theorem for the Busemann function.
Keywords
Cite
@article{arxiv.1308.5926,
title = {Curvature estimates for submanifolds immersed into horoballs and horocylinders},
author = {G. Pacelli Bessa and Jorge H. de Lira and Stefano Pigola and Alberto G. Setti},
journal= {arXiv preprint arXiv:1308.5926},
year = {2015}
}
Comments
To appear in Journal of Mathematical Analysis and Applications