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

show all references

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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