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Volume growth of submanifolds and the Cheeger isoperimetric constant

Authors: Vicent Gimeno and Vicente Palmer
Journal: Proc. Amer. Math. Soc. 141 (2013), 3639-3650
MSC (2010): Primary 53C20, 53C42
Published electronically: June 14, 2013
MathSciNet review: 3080186
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Abstract: We obtain an estimate of the Cheeger isoperimetric constant in terms of the volume growth for a properly immersed submanifold in a Riemannian manifold which possesses at least one pole and sectional curvature bounded from above.

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Additional Information

Vicent Gimeno
Affiliation: Departament de Matemàtiques-INIT, Universitat Jaume I, Castelló, Spain

Vicente Palmer
Affiliation: Departament de Matemàtiques-INIT, Universitat Jaume I, Castelló, Spain

Keywords: Cheeger isoperimetric constant, volume growth, submanifold, Chern-Osserman inequality.
Received by editor(s): April 29, 2011
Received by editor(s) in revised form: December 12, 2011
Published electronically: June 14, 2013
Additional Notes: This work was supported by Fundació Caixa Castelló-Bancaixa Grants P1.1B2006-34 and P1.1B2009-14 and by MICINN grant No. MTM2010-21206-C02-02.
Communicated by: Michael Wolf
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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