The non-parabolicity of infinite volume ends
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- by M. P. Cavalcante, H. Mirandola and F. Vitório PDF
- Proc. Amer. Math. Soc. 143 (2015), 1221-1228 Request permission
Abstract:
Let $M^m$, with $m\geq 3$, be an $m$-dimensional complete non-compact manifold isometrically immersed in a Hadamard manifold $\bar M$. Assume that the mean curvature vector has finite $L^p$-norm, for some $2\leq p\leq m$. We prove that each end of $M$ must either have finite volume or be non-parabolic.References
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Additional Information
- M. P. Cavalcante
- Affiliation: Instituto de Matemática, Universidade Federal de Alagoas, Maceió, AL, CEP 57072-970, Brazil
- MR Author ID: 813473
- Email: marcos.petrucio@pq.cnpq.br
- H. Mirandola
- Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, CEP 21945-970, Brasil
- Email: mirandola@im.ufrj.br
- F. Vitório
- Affiliation: Instituto de Matemática, Universidade Federal de Alagoas, Maceió, AL, CEP 57072-970, Brazil
- Email: feliciano.vitorio@pq.cnpq.br
- Received by editor(s): February 4, 2012
- Received by editor(s) in revised form: April 17, 2013
- Published electronically: November 20, 2014
- Additional Notes: The first and third authors were partially supported by CNPq under the grants 483268/2010-0
- Communicated by: Lei Ni
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 1221-1228
- MSC (2010): Primary 53C40; Secondary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-2014-11901-0
- MathSciNet review: 3293737