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Exit radii of submanifolds from cylindrical domains in warped product manifolds

Published online by Cambridge University Press:  03 June 2015

Hironori Kumura
Hironori Kumura*
Affiliation:
Department of Mathematics, Shizuoka University, Shizuoka 422-8529, Japan, ([email protected])
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Abstract

Let UB(p0; ρ1) × f MV be a cylindrically bounded domain in a warped product manifold := MB × fMV and let M be an isometrically immersed submanifold in . The purpose of this paper is to provide explicit radii of the geodesic balls of M which first exit from UB(p0; ρ1) × fMV for the case in which the mean curvature of M is sufficiently small and the lower bound of the Ricci curvature of M does not diverge to –∞ too rapidly at infinity.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 3 , June 2015 , pp. 559 - 569
Copyright
Copyright © Royal Society of Edinburgh 2015 

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