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Critical metrics of the $ L^{2}$-norm of the scalar curvature


Author: Giovanni Catino
Journal: Proc. Amer. Math. Soc. 142 (2014), 3981-3986
MSC (2010): Primary 53C24, 53C25
DOI: https://doi.org/10.1090/S0002-9939-2014-12238-6
Published electronically: July 28, 2014
MathSciNet review: 3251738
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Abstract: In this paper we investigate complete critical metrics of the $ L^{2}$-norm of the scalar curvature. We prove that any complete critical metric with positive scalar curvature has constant scalar curvature, and we characterize critical metrics with nonnegative scalar curvature in dimensions three and four.


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Additional Information

Giovanni Catino
Affiliation: Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
Email: giovanni.catino@polimi.it

DOI: https://doi.org/10.1090/S0002-9939-2014-12238-6
Keywords: Critical metrics, quadratic functionals
Received by editor(s): December 27, 2012
Published electronically: July 28, 2014
Additional Notes: The author is partially supported by the Italian project FIRB–IDEAS “Analysis and Beyond”
Communicated by: Lei Ni
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.