Curvature estimates for submanifolds immersed into horoballs and horocylinders

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:431

Article

Bessa, G. Pacelli¹  de Lira, Jorge H.¹  Pigola, Stefano²  Setti, Alberto G.² 

[1] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, CE, Brazil

[2] Univ Insubria Como, Sez Matemat DiSAT, I-22100 Como, Italy

关键词: Curvature estimates;    Submanifolds;    Cartan-Hadamard manifolds;    Horoballs;    Horocylinders;   

DOI  :  10.1016/j.jmaa.2015.06.010

来源: Elsevier

【 摘 要 】

We prove mean and sectional curvature estimates 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free