Gradient flows on nonpositively curved metric spaces and harmonic maps

  title={Gradient flows on nonpositively curved metric spaces and harmonic maps},
  author={Uwe F. Mayer},
  journal={Communications in Analysis and Geometry},
  • U. Mayer
  • Published 1998
  • Mathematics
  • Communications in Analysis and Geometry
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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Gradient flows on nonpositively curved metric spaces
  • Ph.D. thesis, University of Utah
  • 1995