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

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (1): 315-332.

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

涂强¹, 陈文艺²

1. Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2016-06-14 修回日期:2017-11-01 出版日期:2018-02-25 发布日期:2018-02-25
作者简介:Qiang TU,E-mail:qiangtu@whu.edu.cn;Wenyi CHEN,E-mail:wychencn@whu.edu.cn
基金资助:
This work is supported by NSF Grant of China (11131005, 11301400) and Hubei Key Laboratory of Applied Mathematics (Hubei University).

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

Qiang TU¹, Wenyi CHEN²

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).

摘要/Abstract

摘要： 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.

关键词: semi-convex function, subgradient, Cartesian current, Hessian measure

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

涂强, 陈文艺. CURRENTS CARRIED BY THE SUBGRADIENT GRAPHS OF SEMI-CONVEX FUNCTIONS AND APPLICATIONS TO HESSIAN MEASURES[J]. 数学物理学报(英文版), 2018, 38(1): 315-332.

Qiang TU, Wenyi CHEN. CURRENTS CARRIED BY THE SUBGRADIENT GRAPHS OF SEMI-CONVEX FUNCTIONS AND APPLICATIONS TO HESSIAN MEASURES[J]. Acta mathematica scientia,Series B, 2018, 38(1): 315-332.

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

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

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