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Lower volume estimates and Sobolev inequalities
Author(s):
Stefano
Pigola;
Giona
Veronelli
Journal:
Proc. Amer. Math. Soc.
138
(2010),
4479-4486.
MSC (2010):
Primary 53C21;
Secondary 46E35
Posted:
July 22, 2010
MathSciNet review:
2680072
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References |
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Additional information
Abstract:
We consider complete manifolds with asymptotically non-negative curvature which enjoy a Euclidean-type Sobolev inequality and we get an explicit lower control on the volume of geodesic balls. In case the amount of negative curvature is small and the Sobolev constant is almost optimal, we deduce that the manifold is diffeomorphic to Euclidean space. This extends previous results by M. Ledoux and C. Xia.
References:
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Additional Information:
Stefano
Pigola
Affiliation:
Dipartimento di Fisica e Matematica, Università dell’Insubria - Como, via Valleggio 11, I-22100 Como, Italy
Email:
stefano.pigola@uninsubria.it
Giona
Veronelli
Affiliation:
Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, I-20133 Milano, Italy
Email:
giona.veronelli@unimi.it
DOI:
10.1090/S0002-9939-2010-10514-2
PII:
S 0002-9939(2010)10514-2
Received by editor(s):
March 12, 2010
Posted:
July 22, 2010
Communicated by:
Michael Wolf
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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