Maximum and Comparison Principles for Convex Functions on the Heisenberg Group
By Cristian E. Gutiérrez, A. Montanari. 2003
53 citations recorded by the source corpus.
Abstract We prove estimates, similar in form to the classical Aleksandrov estimates, for a Monge–Ampère 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–Ampère measures for convex functions in the Heisenberg group.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/7e98861dc32287a4c762a3cd329937a577680041
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- G. Lu
- Juan J. Manfredi
- Petri Juutinen
- Bianca Stroffolini
- Nguyen Huong Lam
- Valentino Magnani
- Caifeng Zhang
- Changyou Wang
In Geometry and Topology
Citations in the corpus
- Convex functions on Carnot groups. (2007, result): “While this manuscript was in preparation we learned about the monotonicity and comparison results of Gutiérrez and Montanari [10, 11] in groups of Heisenberg type.”