Juan Manfredi, Department of Mathematics, University of Pittsburgh.
"Convex Functions in the Heisenberg group"
Convex functions in Euclidean space can be characterized as universal viscosity subsolutions of all homogeneous fully nonlinear second order partial differential equations. This is the starting point to extend the theory of convex functions to non-isotropic spaces, like the Heisenberg group. Proofs are based on the viscosity theory for subelliptic equations and on the role played by the geometric properties of the Carnot-Caratheodory metric.
The results described are joint work with Bianca Stroffolini and Guozhen Lu. A preliminary version of our results is available athttp://www.pitt.edu/~manfredi/quasi.html
TUESDAY, October 22, 2002