In this paper we study integer multiplicity rectifiable currents carried by the subgradient （subdifferential） graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem wit...In this paper we study integer multiplicity rectifiable currents carried by the subgradient （subdifferential） graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. As an application, the structure theorem of the Lagrangian currents for semi-convex functions is given and the k-Hessian measures are calculated by a different method in terms of currents.展开更多
基金supported by NSF Grant of China(11131005,11301400)Hubei Key Laboratory of Applied Mathematics(Hubei University)
文摘In this paper we study integer multiplicity rectifiable currents carried by the subgradient （subdifferential） graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. As an application, the structure theorem of the Lagrangian currents for semi-convex functions is given and the k-Hessian measures are calculated by a different method in terms of currents.
