Functional Analysis techniques in Optimization and Metrization problems

Abstract

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.