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arXiv · 1308.5926

Curvature estimates for submanifolds immersed into horoballs and horocylinders

G. Pacelli Bessa·Jorge H. de Lira·Stefano Pigola·Alberto G. Setti
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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.

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G. Pacelli Bessa, Jorge H. de Lira, Stefano Pigola, Alberto G. Setti. 2015-06-10. Curvature estimates for submanifolds immersed into horoballs and horocylinders. https://arxiv.org/abs/1308.5926

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