PRESCRIPTION OF GAUSS CURVATURE USING OPTIMAL MASS TRANSPORT

Jérôme Bertrand (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper we give a new proof of a theorem by Alexandrov on the Gauss curvature prescription of Euclidean convex sets. This proof is based on the duality theory of convex sets and on optimal mass transport. A noteworthy property of this proof is that it does not rely neither on the theory of convex polyhedra nor on P.D.E. methods (which appeared in all the previous proofs of this result).

Mots clés: Convex bodies; Gauss curvature; optimal mass transport

Domaines: Géométrie métrique [math.MG]

Jérôme Bertrand. PRESCRIPTION OF GAUSS CURVATURE USING OPTIMAL MASS TRANSPORT. Geometriae Dedicata, 2016. ⟨hal-01967244⟩