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Showing 1 to 5 of 5 for “"conformal metric"”.
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Scalar curvature on noncompact complete Riemannian manifolds
… for all x in M. In this thesis, we study a conformal deformation of the given metric g, which makes the scalar curvature of the deformed metric a positive constant. We also study the existence of a complete conformal metric with positive constant scalar curvature. We obtain a sufficient …
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Shape analysis in shape space
… other by a transformation group preserving a geometrical property in which we are interested. Therefore, each deformation is a curve on the high dimensional shape space manifold, and one can classify the deformations by comparison of their corresponding deformation curves in shape space. Towards …
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ANALYZING AND IMPROVING INITIAL DATA FOR BINARY BLACK HOLES
… This will be followed with a discussion of the conformal thin-sandwich decomposition and excision methods which rewrite a portion of the 3+1 decomposition as a well-posed set of elliptic equations and boundary conditions that can be used to determine initial data. Then I will discuss the the …
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Geometric Properties of the Ferrand Metric
… investigate the differentiability of the Ferrand metric-density and find a sufficient condition that implies that the Ferrand metric-density is not differentiable and that the Ferrand Gaussian curvature is negative infinity at a point. We prove that a closed Euclidean ball, closed half-space, or …
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Conformal pseudo-metrics and some applications
… connected to a number of basic open problems in conformal geometry and non-linear PDE. One of our results is a solution to Problem 1 for arbitrary simply connected domains. However, we shall see that our approach has also some other ramifications, for instance to a well-known problem due to …