• Corpus ID: 62824717

Gradient Flows: In Metric Spaces and in the Space of Probability Measures

  title={Gradient Flows: In Metric Spaces and in the Space of Probability Measures},
  author={Luigi Ambrosio and Nicola Gigli and Giuseppe Savar{\'e}},
Notation.- Notation.- Gradient Flow in Metric Spaces.- Curves and Gradients in Metric Spaces.- Existence of Curves of Maximal Slope and their Variational Approximation.- Proofs of the Convergence Theorems.- Uniqueness, Generation of Contraction Semigroups, Error Estimates.- Gradient Flow in the Space of Probability Measures.- Preliminary Results on Measure Theory.- The Optimal Transportation Problem.- The Wasserstein Distance and its Behaviour along Geodesics.- Absolutely Continuous Curves in p… 
Topics on calculus in metric measure spaces
This thesis concerns in some topics on calculus in metric measure spaces, in connection with optimal transport theory and curvature-dimension conditions. We study the continuity equations on metric
  • L. Ambrosio
  • Mathematics
    Proceedings of the International Congress of Mathematicians (ICM 2018)
  • 2019
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