141 citations · 555 across the 57 of their papers we have counts for
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math.DG2021★ 2 cited
Moon in a puddle and the four-vertex theorem
Anton Petrunin, Sergio Zamora Barrera
We present a proof of the Moon in a puddle theorem, and use its key lemma to prove a generalization of the four-vertex theorem.
math.DG2021
Self-crossing geodesics
Anton Petrunin
We discuss self-crossing patterns of closed geodesics on a convex surface.
math.DG2021★ 8 cited
About every convex set in any generic Riemannian manifold
Alexander Lytchak, Anton Petrunin
We give a necessary condition on a geodesic in a Riemannian manifold that can run in some convex hypersurface. As a corollary we obtain peculiar properties that hold true for every…