# Gradient flows on nonpositively curved metric spaces and harmonic maps

@article{Mayer1998GradientFO, title={Gradient flows on nonpositively curved metric spaces and harmonic maps}, author={Uwe F. Mayer}, journal={Communications in Analysis and Geometry}, year={1998}, volume={6}, pages={199-253} }

The notion of gradient flows is generalized to a metric space setting without any linear structure. The metric spaces considered are a generalization of Hilbert spaces, and the properties of such metric spaces are used to set up a finite-difference scheme of variational form. The proof of the Crandall–Liggett generation theorem is adapted to show convergence. The resulting flow generates a strongly continuous semigroup of Lipschitz-continuous mappings, is Lipschitz continuous in time for…

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