MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
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 '10 at 19:06
Maybe someone has written lecture notes about this subject, it doesn't have to be a book. – Jonas Teuwen Oct 21 '10 at 19:18
up vote 6 down vote accepted

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

share|cite|improve this answer
Looks good! Thanks for the links. Interestingly P. Clément is an emeritus professor at my department. – Jonas Teuwen Oct 21 '10 at 21:48

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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.