141 citations · 555 across the 57 of their papers we have counts for
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Lectures on Alexandrov spaces with curvature bounded below
Vitali Kapovitch, Nina Lebedeva, Anton Petrunin
An introduction to Alexandrov spaces with curvature bounded below. Topics include various comparison conditions, the globalization theorem, tangent spaces and spaces of directions,…
Quadratic metric comparisons
Nina Lebedeva, Anton Petrunin, Vladimir Zolotov
We study the effects on length spaces imposed by quadratic inequalities on the six distances between the points in every quadruple.
Gromov's tori are optimal
Anton Petrunin
We give an optimal bound on normal curvatures of immersed n-torus in a Euclidean ball of large dimension.
Polyhedral approximations of Riemannian manifolds
Anton Petrunin
We give a condition on the curvature tensors of Riemannian manifolds that admit Lipschitz approximation by polyhedral metrics with curvature bounded below or above. We show that th…
Curvature tensor of smoothable Alexandrov spaces
Nina Lebedeva, Anton Petrunin
We prove weak convergence of curvature tensors of Riemannian manifolds for converging noncollapsing sequences with a lower bound on sectional curvature.
Five-point Toponogov theorem
Nina Lebedeva, Anton Petrunin
We give an if-and-only-if condition on a five-point metric spaces that admit embeddings into nonnegatively curved Riemannian manifolds.