# American Institute of Mathematical Sciences

2010, 17: 122-124. doi: 10.3934/era.2010.17.122

## Curvature bounded below: A definition a la Berg--Nikolaev

 1 St. Petersburg Department of V.A. Steklov Mathematical Institute, Fontanka 27, 191023, St. Petersburg, Russian Federation 2 Department of Mathematics, Penn State University, University Park, PA 16802, United States

Received  August 2010 Revised  September 2010 Published  October 2010

We give a new characterization of spaces with nonnegative curvature in the sense of Alexandrov.
Citation: Nina Lebedeva, Anton Petrunin. Curvature bounded below: A definition a la Berg--Nikolaev. Electronic Research Announcements, 2010, 17: 122-124. doi: 10.3934/era.2010.17.122
##### References:
 [1] I. D. Berg and I. G. Nikolaev, Quasilinearization and curvature of Aleksandrov spaces,, Geom. Dedicata, 133 (2008), 195.  doi: doi:10.1007/s10711-008-9243-3.  Google Scholar [2] Yu. Burago, M. Gromov and G. Perelman, A. D. Aleksandrov spaces with curvatures bounded below, (Russian), Uspekhi Mat. Nauk, 47 (1992), 3.   Google Scholar [3] T. Foertsch, A. Lytchak and V. Schroeder, Nonpositive curvature and the Ptolemy inequality,, Int. Math. Res. Not. (IMRN), 2007 (2007).   Google Scholar [4] M. Gromov, "Metric Structures for Riemannian and Non-Riemannian Spaces,", Progress in Mathematics, 152 (1999).   Google Scholar [5] U. Lang and V. Schroeder, Kirszbraun's theorem and metric spaces of bounded curvature,, Geom. Funct. Anal., 7 (1997), 535.  doi: doi:10.1007/s000390050018.  Google Scholar [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.   Google Scholar

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##### References:
 [1] I. D. Berg and I. G. Nikolaev, Quasilinearization and curvature of Aleksandrov spaces,, Geom. Dedicata, 133 (2008), 195.  doi: doi:10.1007/s10711-008-9243-3.  Google Scholar [2] Yu. Burago, M. Gromov and G. Perelman, A. D. Aleksandrov spaces with curvatures bounded below, (Russian), Uspekhi Mat. Nauk, 47 (1992), 3.   Google Scholar [3] T. Foertsch, A. Lytchak and V. Schroeder, Nonpositive curvature and the Ptolemy inequality,, Int. Math. Res. Not. (IMRN), 2007 (2007).   Google Scholar [4] M. Gromov, "Metric Structures for Riemannian and Non-Riemannian Spaces,", Progress in Mathematics, 152 (1999).   Google Scholar [5] U. Lang and V. Schroeder, Kirszbraun's theorem and metric spaces of bounded curvature,, Geom. Funct. Anal., 7 (1997), 535.  doi: doi:10.1007/s000390050018.  Google Scholar [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.   Google Scholar
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