Convex Functions on the Heisenberg Group
نویسندگان
چکیده
Convex functions in Euclidean space can be characterized as universal viscosity subsolutions of all homogeneous fully nonlinear second order elliptic partial differential equations. This is the starting point we have chosen for a theory of convex functions on the Heisenberg group.
منابع مشابه
On the Second Order Derivatives of Convex Functions on the Heisenberg Group
A classical result of Aleksandrov asserts that convex functions in Rn are twice differentiable a.e., and a rst step to prove it is to show that these functions have second order distributional derivatives which are measures, see [4, pp. 239-245]. On the Heisenberg group, and more generally in Carnot groups, several notions of convexity have been introduced and compared in [3] and [7], and Ambro...
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