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Electronic Research Announcements in Mathematical Sciences (ERA-MS)
 

Curvature bounded below: A definition a la Berg--Nikolaev
Pages: 122 - 124, January 2010

doi:10.3934/era.2010.17.122      Abstract        References        Full text (94.9K)           Related Articles

Nina Lebedeva - St. Petersburg Department of V.A. Steklov Mathematical Institute, Fontanka 27, 191023, St. Petersburg, Russian Federation (email)
Anton Petrunin - Department of Mathematics, Penn State University, University Park, PA 16802, United States (email)

1 I. D. Berg and I. G. Nikolaev, Quasilinearization and curvature of Aleksandrov spaces, Geom. Dedicata, 133 (2008), 195-218.       
2 Yu. Burago, M. Gromov and G. Perelman, A. D. Aleksandrov spaces with curvatures bounded below, (Russian) Uspekhi Mat. Nauk, 47 (1992), 3-51, 222; translation in Russian Math. Surveys 47 (1992), 1-58.       
3 T. Foertsch, A. Lytchak and V. Schroeder, Nonpositive curvature and the Ptolemy inequality, Int. Math. Res. Not. (IMRN), 2007 (2007), Art. ID rnm100, 15 pp.       
4 M. Gromov, "Metric Structures for Riemannian and Non-Riemannian Spaces," Progress in Mathematics, vol. 152, Birkhäuser Boston, Inc., Boston, MA, 1999.       
5 U. Lang and V. Schroeder, Kirszbraun's theorem and metric spaces of bounded curvature, Geom. Funct. Anal., 7 (1997), 535-560.       
6 Takashi Sato, An alternative proof of Berg and Nikolaev's characterization of $CAT(0)$-spaces via quadrilateral inequality, Arch. Math. (Basel), 93 (2009), 487-490.       

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