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math.AP2003★ 10 cited
On the second order derivatives of convex functions on the Heisenberg group
Cristian E. Gutierrez, Annamaria Montanari
In the Euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result…
math.AP2003
Maximum and comparison principles for convex functions on the Heisenberg group
Cristian E. Gutierrez, Annamaria Montanari
We prove estimates, similar in form to the classical Aleksandrov estimates, for a Monge-Ampere type operator on the Heisenberg group. A notion of normal mapping does not seem to be…