scholarly journals Hyperbolic sets that are not contained in a locally maximal one

2017 ◽  
Vol 37 (9) ◽  
pp. 4923-4941
Author(s):  
Adriana da Luz ◽  
Keyword(s):  
Locally Maximal ◽  
Hyperbolic Sets

scholarly journals ON UNIQUENESS AND DIFFERENTIABILITY IN THE SPACE OF YAMABE METRICS

2005 ◽  
Vol 07 (03) ◽  
pp. 299-310 ◽  
Author(s):  
MICHAEL T. ANDERSON
Keyword(s):  
Scalar Curvature ◽  
Sufficient Conditions ◽  
Locally Maximal ◽  
Generic Set ◽  
Scalar Curvature Functional

It is shown that there is a unique Yamabe representative for a generic set of conformal classes in the space of metrics on any manifold. At such classes, the scalar curvature functional is shown to be differentiable on the space of Yamabe metrics. In addition, some sufficient conditions are given which imply that a Yamabe metric of locally maximal scalar curvature is necessarily Einstein.

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