Un principe de concentration-compacité pour les suites de surfaces Riemanniennes
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Uniformly Convex Metric Spaces
Martin Kell (2014)
Analysis and Geometry in Metric Spaces
In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology, called coconvex topology, agrees with the usually weak topology in Banach spaces. An example of a CAT(0)-space with weak topology which is not Hausdorff is given. In the end existence and uniqueness...
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