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math.DG2026
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.
math.DG2026
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.
math.HO2026
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…