An extension of Alexandrovʼs theorem on second derivatives of convex functions

Alberti, 1999, A geometrical approach to monotone functions in Rn, Math. Z., 230, 259, 10.1007/PL00004691 Alexandrov, 1939, Almost everywhere existence of the second differential of a convex function and some properties of convex surfaces connected with it, Leningrad Univ. Ann. (Math. Ser.), 6, 3 Calderón, 1961, Local properties of elliptic partial differential equations, Studia Math., 20, 171, 10.4064/sm-20-2-181-225 Evans, 1992 Folland, 1999 Fu, 1989, Monge–Ampère functions I, Indiana Univ. Math. J., 38, 745, 10.1512/iumj.1989.38.38035 Fu, 1989, Monge–Ampère functions II, Indiana Univ. Math. J., 38, 773, 10.1512/iumj.1989.38.38036 Gilbarg, 1983 Giusti, 1984 Hutchinson, 1986, A remark on the nonuniqueness of tangent cones, Proc. Amer. Math. Soc., 97, 184 Jerrard, 2008, Some remarks on Monge–Ampère functions Jerrard, 2010, Some rigidity results related to Monge–Ampère functions, Canad. J. Math., 62, 320, 10.4153/CJM-2010-019-8