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Some characterizations of space-forms


Authors: Stefano Pigola, Marco Rigoli and Alberto G. Setti
Journal: Trans. Amer. Math. Soc. 359 (2007), 1817-1828
MSC (2000): Primary 53C21; Secondary 35J60, 35B05
DOI: https://doi.org/10.1090/S0002-9947-06-04091-8
Published electronically: November 3, 2006
Erratum: Tran. Amer. Math. Soc. 360 (2008), 3943-3944.
MathSciNet review: 2272150
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Abstract | References | Similar Articles | Additional Information

Abstract: Integral conditions on the traceless Ricci tensor are used to characterize Euclidean and hyperbolic spaces among complete, locally conformally flat manifolds of constant scalar curvature. The main tools are vanishing-type results for $ L^{p}$-solutions of a large class of differential inequalities. Further applications of the technique are also given.

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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

Marco Rigoli
Affiliation: Dipartimento di Matematica, Università di Milano, via Saldini 50, I-20133 Milano, Italy
Email: rigoli@mat.unimi.it

Alberto G. Setti
Affiliation: Dipartimento di Fisica e Matematica, Università dell’Insubria - Como, via Valleggio 11, I-22100 Como, Italy
Email: alberto.setti@uninsubria.it

DOI: https://doi.org/10.1090/S0002-9947-06-04091-8
Keywords: Space forms, vanishing theorems, isolation phenomena
Received by editor(s): January 29, 2005
Published electronically: November 3, 2006
Dedicated: Dedicated to the memory of Franca Burrone Rigoli
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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