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New properties of convex functions in the Heisenberg group

Author(s): Nicola Garofalo; Federico Tournier
Journal: Trans. Amer. Math. Soc. 358 (2006), 2011-2055.
MSC (2000): Primary 35H20; Secondary 26B25, 20F18
Posted: December 20, 2005
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Abstract: We prove some new properties of the weakly $ H$-convex functions recently introduced by Danielli, Garofalo and Nhieu. As an interesting application of our results we prove a theorem of Busemann-Feller-Alexandrov type in the Heisenberg groups $ \mathbb{H}^n$, $ n=1,2$.

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Additional Information:

Nicola Garofalo
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: garofalo@math.purdue.edu

Federico Tournier
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: tournier@math.purdue.edu, fedeleti@aim.com

DOI: 10.1090/S0002-9947-05-04016-X
PII: S 0002-9947(05)04016-X
Keywords: Sub-elliptic fully nonlinear equations, monotonicity of Monge-Amp\`ere measures, sub-elliptic cones, Busemann-Feller-Alexandrov theorem
Received by editor(s): February 13, 2004
Posted: December 20, 2005
Additional Notes: The first author was supported in part by NSF Grants No. DMS-0070492 and No. DMS-0300477
This work was presented by the first author in a Colloquium lecture at the University of Missouri, Columbia, in April 2003, and at the AMS Meeting at San Francisco State University in May 2003
Copyright of article: Copyright 2005, American Mathematical Society

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