What is the/a main reference book for spaces with curvature bounded from below (CBB spaces/spaces with curvature $\geq \kappa$ in the sense of Alexandrov)? Looking for an up to date reference.
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$\begingroup$ Up to my English handbook it should be "..: metric spaces.." so I edited your title. $\endgroup$– user64494Commented Jun 17, 2019 at 16:56
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$\begingroup$ According to my experience of speaking and writing English, it should be "according to my English handbook". Motes and beams, eh? $\endgroup$– Yemon ChoiCommented Jun 19, 2019 at 19:26
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1 Answer
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You may check preliminary version of our book/3. Otherwise do "Alexandrov spaces with curvature bounded below" by Burago, Gromov, and Perelman and "Alexandrov's space with curvatures bounded from below II" by Perelman. There are some improvements of the results and proofs, but these two papers are still the main reference source; plus there are surveys by one by Plaut and one by me.
There are also reader friendly introductions one by Shiohama and a chapter in Metric geometry by Burago, Burago and Ivanov.
answered Jun 17, 2019 at 21:48