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

@inproceedings{Ambrosio2005GradientFI, title={Gradient Flows: In Metric Spaces and in the Space of Probability Measures}, author={Luigi Ambrosio and Nicola Gigli and Giuseppe Savar{\'e}}, year={2005} }

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…

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