8 citations · 10 across the 8 of their papers we have counts for
9 papers
Milnor's cartography problem
Anton Petrunin
We solve John Milnor's problem: among all convex regions of a given area on the sphere, the round disk requires the greatest distortion in cartographic projections onto the plane.
Nash's theorem via Günther's trick
Anton Petrunin
We present a proof of Nash's smooth embedding theorem with an emphasis on accessibility and rigor.
A translation of "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…
A gallery of open problems in geometry that keep me puzzled and amused
Anton Petrunin
This is a collection of open questions in geometry that I think of as \textit{puzzles}: they stick to my brain --- I see grips, but no spare hands. Puzzle-charm is the only criteri…
Veronese minimizes normal curvatures
Anton Petrunin
Suppose M is a closed submanifold in a Euclidean ball of sufficiently large dimension. We give an optimal bound on the normal curvatures, guaranteeing that M is a sphere. The borde…
Tubed embeddings
Anton Petrunin
We consider the following question: When does a Riemannian manifold admit an embedding with a uniformly thick tubular neighborhood in another Riemannian manifold of large dimension…
Metric geometry on manifolds: two lectures
Anton Petrunin
We discuss Besicovitch inequality, width, and systole of manifolds.
Alexandrov geometry: foundations
Stephanie Alexander, Vitali Kapovitch, Anton Petrunin
Alexandrov spaces are defined via axioms similar to those given by Euclid. The Alexandrov axioms replace certain equalities with inequalities. Depending on the signs of the inequal…
An invitation to Alexandrov geometry: CAT(0) spaces
Stephanie Alexander, Vitali Kapovitch, Anton Petrunin
Our goal is to show the beauty and power of Alexandrov geometry by reaching interesting applications and theorems with a minimum of preparation. The topics include 1. Reshetnyak's…