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

2015/12/30 by Qiang Tu, Tu, Qiang, Wenyi Chen +1
Mathematics · #Advanced Topology and Set Theory #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.DG

paper · pdf · doi:10.48550/arxiv.1512.08850

15 pages

openalex publication_date 2015/12/30 · arxiv created 2016/01/13 · arxiv updated 2016/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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