We prove mean and sectional curvature estimates for submanifolds confined into either a horocylinder of N×. 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.

Bessa G., P., de Lira Jorge, H., Pigola, S., Setti Alberto, G. (2015). Curvature estimates for submanifolds immersed into horoballs and horocylinders. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 431(2), 1000-1007 [10.1016/j.jmaa.2015.06.010].

Curvature estimates for submanifolds immersed into horoballs and horocylinders

Pigola Stefano
;
2015

Abstract

We prove mean and sectional curvature estimates for submanifolds confined into either a horocylinder of N×. 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.
Articolo in rivista - Articolo scientifico
Curvature estimates; Submanifolds; Cartan–Hadamard manifolds; Horoballs; Horocylinders
English
2015
431
2
1000
1007
reserved
Bessa G., P., de Lira Jorge, H., Pigola, S., Setti Alberto, G. (2015). Curvature estimates for submanifolds immersed into horoballs and horocylinders. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 431(2), 1000-1007 [10.1016/j.jmaa.2015.06.010].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/271354
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