141 citations · 555 across the 57 of their papers we have counts for
57 papers
Metric foundations of geometry
Nina Lebedeva, Anton Petrunin
A metric space is called all-set-homogeneous if every isometry between two of its subsets extends to an isometry of the whole space. We classify all-set-homogeneous geodesic spaces…
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,…
An isoperimetric inequality for mean shadow
Roman Karasev, Anton Petrunin, Alexander Plakhov
We prove an isoperimetric inequality in terms of the mean shadow area.
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.
Alexandrov's embedding theorem
Nina Lebedeva, Anton Petrunin
Written for the book "Mathematicians from Saint Petersburg and their theorems".