A Variational Approach to Gradient Flows in Metric Spaces
In this note we report on a new variational principle for Gradient Flows in metric spaces. This new variational formulation consists in a functional defined on entire trajectories whose minimizers converge, in the case in which the energy is geodesically convex, to curves of maximal slope. The key point in the proof is a reformulation of the problem in terms of a dynamic programming principle combined with suitable a priori estimates on the minimizers. The abstract result is applicable to a large...