Calculus of Variations and Geometric Measure Theory
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G. Catino

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

created by catino on 12 Apr 2012
modified on 27 Jun 2013


Accepted Paper

Inserted: 12 apr 2012
Last Updated: 27 jun 2013

Journal: Proc. Amer. Math. Soc.
Year: 2013


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 dimension three and four.


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