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math.MG2026
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…
math.DG2026
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,…
math.MG2026
An isoperimetric inequality for mean shadow
Roman Karasev, Anton Petrunin, Alexander Plakhov
We prove an isoperimetric inequality in terms of the mean shadow area.