Functional Analysis techniques in Optimization and Metrization problems
We give an introduction on the main subjects of metric geometry, derived (conceptually) from the Riemannian theory, in the setting of Lie groups groups G modeled by locally convex spaces, and admitting continuous Finsler metrics. The focus is put in the functional analysis techniques, since such norms are usually not differentiable and the variational calculus is not at hand. These techniques, however, allow us to retain some of the fine results of the tensor calculus, and even in the absence of linear connections, we show in the setting of Lie groups with a bi-invariant metric, how some results such as the minimality of one-parameter groups, can be recovered using such techniques.
KeywordsLie group locally convex space Finsler metric invariant metric geodesic one-parameter group isometry group.
Mathematics Subject Classification (2000)Primary 22E65 58B20 Secondary 53C22 47B10 58D05.
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