This entry is about length spaces behaving like having sectional curvature bounded below, named after Alexander Alexandrov. For specialization topologies on preorders see instead at Alexandroff spaces, named after Paul Alexandroff.
synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
In differential geometry, Alexandrov spaces are certain locally compact complete length spaces which generalize Riemannian manifolds whose sectional curvature is bounded below by some real number.
Katsuhiro Shiohama, An Introduction to the Geometry of Alexandrov spaces, lecture at Daewoo Workshop on Differential Geometry (1992) [pdf]
Yukio Otsu, Differential geometric aspects of Alexandrov spaces, in: Comparison Geometry, MSRI publications 30, Cambridge University Press (1997) [pdf, ISBN-10: 0-521-59222-4]
Wikipedia, Alexandrov space
Grigori Perelman, Elements of Morse theory on Alexandrov spaces, St. Petersburg Math. J. 5 1 (1994) 205–213 [mathet:aa374]
Grigori Perelman, DC structure on Alexandrov spaces [pdf, pdf]
Yuri Burago, Mikhail Gromov, Grigori Perelman, Alexandrov spaces with curvature bounded below, Russ. Math. Surveys 41 3 (1992) 1-54 [doi:10.1070/RM1992v047n02ABEH000877, pdf]
MathOverflow, Details of Perelman’s example about soul of Alexandrov space (2010) [MO:q/22105]
MathOverflow, Metrically singular Alexandrov space (2011) [MO:q/67046],
MathOverflow, Is there Domain Invariance for Alexandrov spaces? (2010) [MO:q/21512]
MathOverflow, Rigidity of triangle comparison in Alexandrov spaces (2010) [MO:q/44943]
Last revised on June 2, 2024 at 05:58:30. See the history of this page for a list of all contributions to it.