# Questions tagged [alexandrov-geometry]

Alexandrov geometry studies non smooth analogues of Riemannian manifolds with curvature bounded from below or above. It includes spaces with curvature bounded below (briefly $\mathrm{CBB}[\kappa]$) and spaces with curvature bounded above (briefly $\mathrm{CAT}[\kappa]$).

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### Isometric imbedding of a 2-disk into Euclidean 3-space

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### Is a cap an Alexandrov space?

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### Reference to equivariant Gromov-Hausdorff convergence

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### Regularity of the distance function to a compact set in an Alexandrov space

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### Essential singularities in an Alexandrov space

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### Essential singular set of an Alexandrov space

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### Topology of compact Alexandrov spaces with nonnegative curvature

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### Does codimension-1 collapsing with bounded curvature have boundary?

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### Rigidity for convex surfaces in elliptic/hyperbolic space

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### Completion of an Alexandrov space

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### Topology of $3$-dimensional noncompact Alexandrov space with sec $\ge 0$

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### Semiconcavity estimate for the squared distance on a compact Riemannian manifold

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### Nearby convex set in a nearby space

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### Alexandrov spaces of zero curvature

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### Convex separation in CAT(0) spaces

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### Translation lengths in CAT(0) spaces

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### Convex spherical neighborhood in Alexandrov spaces

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### Toponogov's theorem in the Alexandrov space with respect to a compact set

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### Uniqueness of geodesics in the Alexandrov space

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### Ball Covering Property in Non-negatively Curved Spaces [Reference Request]

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### About the paper "Elements of Morse theory on Alexandrov spaces"

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### Convexity of the scalar product in the Alexandrov space

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### Concavity of the distance function to the boundary of Alexandrov space

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### When Riemannian manifold with boundary is Alexandrov space?

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### Geodesic line with endpoints in interior of Riemannian manifold or Alexandrov space

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### Tangent cone of metric graph

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### CBB inequality and two comparison triangles / 4-point condition for CBB spaces

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### gradient curve $\gamma$ defined on $(-T,0]$, can't be extended from $\gamma(-T)$?

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### Unbounded curvature implies infinite diameter on complete metric spaces

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### Estimate of volume of a ball on the boundary of Riemannian manifold

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### A Lipschitz limit of Riemannian metrics with curvature in $[-1,1]$

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### When is the quotient of a geodesic space again a geodesic space?

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### Continuity of volume of boundary of Riemannian manifolds in the Gromov-Hausdorff sense

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### Measure of the boundary of Alexandrov space

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### Dimension of Alexandrov space which is homeomorphic to a manifold

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### Neighborhood of $(n,\delta)$-strained point in Alexandrov space homeomorphic to $\mathbb{R}^n$, how big is $\delta$?

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### Pointed version of Perelman stability theorem

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### Why 2-tori with Gauss curvature $\geq -1$ cannot collapse to segment?

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### Approximation of 2-dimensional Alexandrov spaces

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### A.D. Alexandrov imbedding theorem for metrics with symmetry

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### Inequalities on 4 points in metric spaces with curvature bounded below (CBB)

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### Reference request: metric spaces with curvature bounded from below (CBB) spaces

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### In a manifold, $\angle xpy>\frac{\pi}{2}$, for $q$ on $px$ or $py$, $B_q(r)$ homeomorphic to $B_p(r)$?

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### Non-collapsed Alexandrov spaces, level surface of regular map homeo to its lifting?

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### Is there Brownian motion on Alexandrov spaces?

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### Gluing hexagons to get a locally CAT(0) space

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### Does geometrization of Alexandrov 3-spaces follow from that of 3-orbifolds?

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### Contractibility of balls in Alexandrov spaces

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### Discrete approximations of Riemannian manifolds

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