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arXiv · 1512.08850

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

Qiang Tu·Wenyi Chen
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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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Qiang Tu, Wenyi Chen. 2016-01-13. Currents carried by the subgradient graphs of semi-convex functions and applications to Hessian measure. https://arxiv.org/abs/1512.08850

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