From the 1 of 9 linked papers with an AI index.
9 papers
Lectures on Alexandrov spaces with curvature bounded below
Vitali Kapovitch, Nina Lebedeva, Anton Petrunin
This work is an introductory exposition on Alexandrov spaces with curvature bounded below, covering comparison conditions, the globalization theorem, tangent spaces, gradient flows…
An isoperimetric inequality for mean shadow
Roman Karasev, Anton Petrunin, Alexander Plakhov
We prove an isoperimetric inequality in terms of the mean shadow area.
What is differential geometry: curves and surfaces
Anton Petrunin, Sergio Zamora Barrera
These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- t…
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.
Trees meet octahedron comparison
Nina Lebedeva, Anton Petrunin
We show that trees and their products meet octahedron comparison.
Euclidean plane and its relatives; a minimalist introduction
Anton Petrunin
The book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalist. List of topics: Euclidean geometry: Th…