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What is a good introduction in gradient flows in metric spaces? I know the book Gradient flows: in metric spaces and in the space of probability measures by Luigi Ambrosio, Nicola Gigli and Giuseppe Savaré, but is too hard for an introduction (for me). I'm looking for something with a similar content.

edited Oct 21 2010 at 18:09

Jonas Teuwen

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	But this is a hard topic. A new one indeed. I doubt that there be any easier book on this subject. – Denis Serre Oct 21 2010 at 19:06
	Maybe someone has written lecture notes about this subject, it doesn't have to be a book. – Jonas Teuwen Oct 21 2010 at 19:18

mathphysicist · Accepted Answer · 2010-10-21 21:06:19Z UTC

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Here are some links to the online lecture notes which are hopefully more accessible than the book you mentioned:

Lecture Notes on Gradient Flows and Optimal Transport by S. Daneri
An Introduction to Gradient Flows in Metric Spaces and Introduction to Gradient Flows in Metric Spaces (II) by P. Clément

answered Oct 21 2010 at 21:06

mathphysicist

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Looks good! Thanks for the links. Interestingly P. Clément is an emeritus professor at my department. – Jonas Teuwen Oct 21 2010 at 21:48

Bob Pego · Answer 2 · 2010-10-30 17:54:26Z UTC

The book Topics in Optimal Transportation by Cédric Villani is not exactly on this topic but is very well written and contains a lot of related material good for background, motivation and applications. The book of Ambrosio, Gigli and Savaré is indeed pretty dry, but the results they established improved considerably on what was available in the literature.

The notes of Daneri and Savaré look good --- Savaré's presentations in a summer school this past June are available here.

Textbooks or notes on gradient flows in metric spaces.

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