Trudinger, NeilZhang, Wei2015-12-130022-1236http://hdl.handle.net/1885/72387In this paper, we study the properties of k-convex functions on the Heisenberg group Hn, for 1 ≤ k≤ 2n and prove the weak continuity of k-Hessian measures with respect to local uniform convergence in the Heisenberg setting. Our approach through monotoKeywords: Heisenberg group; Hessian measures; Monotonicity formula; Weak convergence201310.1016/j.jfa.2013.02.0192016-02-24