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IMMERSION OF MANIFOLDS WITH UNBOUNDED IMAGE AND A MODIFIED MAXIMUM PRINCIPLE OF YAU
Published online by Cambridge University Press: 01 October 2008
Abstract
Let N be a complete Riemannian manifold isometrically immersed into a Hadamard manifold M. We show that the immersion cannot be bounded if the mean curvature of the immersed manifold is small compared with the curvature of M and the Laplacian of the distance function on N grows at most linearly. The latter condition is satisfied if the Ricci curvature of N does not approach too fast. The main tool in the proof is a modification of Yau’s maximum principle.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 78 , Issue 2 , October 2008 , pp. 285 - 291
- Copyright
- Copyright © 2008 Australian Mathematical Society
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