I’m currently reading Burago, Burago, Ivanov’s book A Course in Metric Geometry. I’m really enjoying it so far - what would be a good continuation to the book once I’m done?

  • $\begingroup$ Hi! What's your background? $\endgroup$ Jun 5 '19 at 18:41
  • $\begingroup$ Hi! I’ve studied analysis from Stein and Shakarchi book 3 and 4. Also some riemannian geometry from Lee and a bit of geometric measure theory. I’ve also read Clara Loh’s book on geometric group theory, which seems to be quite related to this topic. $\endgroup$ Jun 5 '19 at 18:53
  • $\begingroup$ That’s all of the relevant background I can think of for now.. $\endgroup$ Jun 5 '19 at 18:53
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    $\begingroup$ see arxiv.org/abs/1903.08539. $\endgroup$ Jun 6 '19 at 10:30

As you have been reading Loh's book, I recommend you take a look at Metric spaces of non-positive curvature by M. Bridson and A. Häfliger.

See also An invitation to Alexandrov geometry: CAT(0) spaces by S. Alexander, V. Kapovitch and A. Petrunin, or its older version.

  • $\begingroup$ Looks good, thanks! $\endgroup$ Jun 5 '19 at 19:21
  • $\begingroup$ @AntonPetrunin Hi, I took a look to your notes and I think they are a very good introduction. Since they were already mentioned in another comment, I have added them to my answer to make them easier to find. $\endgroup$ May 11 '20 at 8:24
  • $\begingroup$ The book mentioned by Igor Belegradek is a bigger project, so far only draft is available; it is more like reference source (not an introduction). $\endgroup$ May 11 '20 at 18:07
  • $\begingroup$ @AntonPetrunin I see, it is good to know! $\endgroup$ May 23 '20 at 6:31
  • $\begingroup$ @AntonPetrunin Why is the Springer version much shorter than the one on Arxiv ? $\endgroup$ Jun 18 '20 at 13:54

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