5 papers · 1 filter
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.
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…
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…
A gallery of open problems in geometry that keep me puzzled and amused
Anton Petrunin
This is a collection of open problems in geometry that I think of as puzzles: they stick to my brain -- I see many grips, but no spare hands. Puzzle-charm is the only criterion for…
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…