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math.MG2010
Infinite curvature on typical convex surfaces
Karim Adiprasito
Solving a long-standing open question in convex geometry, we will show that typical convex surfaces contain points of infinite curvature in all tangent directions. To prove this, w…
math.MG2010
Characterization of polytopes via tilings with similar pieces
Karim Adiprasito
Generalizing results by Valette, Zamfirescu and Laczkovich, we will prove that a convex body is a polytope if there are sufficiently many tilings which contain a tile similar t…