# Currents carried by the subgradient graphs of semi-convex functions and applications to Hessian measure

Research paper by Qiang Tu, Wenyi Chen

Indexed on: 13 Jan '16Published on: 13 Jan '16Published in: Mathematics - Differential Geometry

#### Abstract

In this paper we study integer multiplicity rectifiable currents carried by the subgradient (subdifferential) graphs of semi-convex functions on a $n$-dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. As an application, the $k$-Hessian measures are calculated by a different method in terms of currents.