Recent Advances in Pure and Applied Mathematics by Unknown

Author:Unknown
Language: eng
Format: epub, pdf
ISBN: 9783030413217
Publisher: Springer International Publishing

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where d e denotes the Riemannian distance function in the metric e with respect to a fixed origin 0 ∈ M. These functional spaces share several of the properties of the usual Sobolev spaces, such as the embedding theorems and continuous multiplications properties [21].

In order to formulate the TSP in this context, we will again consider the linearisation of the RTSE around umbilical solutions of the constraint equations (g, K = αg). We will then set the momentum density to zero, i.e., S = 0, and thus we have a prescribed scalar curvature equation for g, of the form

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