Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (1): 315-332.

• Articles • Previous Articles     Next Articles

CURRENTS CARRIED BY THE SUBGRADIENT GRAPHS OF SEMI-CONVEX FUNCTIONS AND APPLICATIONS TO HESSIAN MEASURES

Qiang TU1, Wenyi CHEN2   

  1. 1. Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China;
    2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2016-06-14 Revised:2017-11-01 Online:2018-02-25 Published:2018-02-25
  • Supported by:
    This work is supported by NSF Grant of China (11131005, 11301400) and Hubei Key Laboratory of Applied Mathematics (Hubei University).

Abstract: 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.

Key words: semi-convex function, subgradient, Cartesian current, Hessian measure

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