Maximum and comparison principles for convex functions on the Heisenberg group

Details Maximum and comparison principles for convex functions on the Heisenberg group Maximum and comparison principles for convex functions on the Heisenberg group

2003-06-03

arxiv.org/abs/math/0306059v1

Mathematics

Analysis of PDEs

The results in this paper and the ideas of their proofs have been presented in the following talks: Analysis Seminar, Temple U

Scientific paper

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 available in this context and the method of proof uses integration by parts and oscillation estimates that lead to the construction of an analogue of Monge-Ampere measures for convex functions in the Heisenberg group.

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