7
$\begingroup$

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?

$\endgroup$
4
  • $\begingroup$ 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
  • 3
    $\begingroup$ see arxiv.org/abs/1903.08539. $\endgroup$ Jun 6 '19 at 10:30
9
$\begingroup$

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.

$\endgroup$
6
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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