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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.

Can someone make this a community wiki? I cannot find how you have to do that...

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    I found the same problem (make it a community wiki) in my last question and I don't know.2010-10-20
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    See this answer http://meta.math.stackexchange.com/questions/941/community-wiki-checkbox-disappeared/942#9422010-10-20
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    @Américo Tavares: Thanks for the link.2010-10-20
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    Since I don't get any answers here, would this be an okay question for MO (community wiki)?2010-10-21
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    @Jonas: I think you should try.2010-10-21
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    I got a reply there, this can be closed. http://mathoverflow.net/questions/43083/textbooks-or-notes-on-gradient-flows-in-metric-spaces2010-10-21

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To close this question I will post the answer which I got at Mathoverflow.

I have read Philippe Clément's notes on gradient flows in metric spaces.

Another nice book which I have found is the book "Optimal Transport, old and new" by Cédric Villani". Nice book. It is in the Yellow Sale in Europe until the end of July.

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Also there are notes by Onno van Gaans, partly based on Clément's notes.

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    I know those, I did the course he gave before the course lectures started by studying Clément's notes.2011-07-02