# A potential theory for the k-curvature equation

## TL;DR

This paper develops a potential theory for the k-curvature equation, linking PDE methods to curvature measures and establishing measure continuity for specific functions.

## Contribution

It introduces a novel potential theory for the k-curvature equation, connecting PDE techniques with curvature measure analysis.

## Key findings

- Established a measure assignment for k-curvature subharmonic functions.
- Proved weak continuity of the measure for these functions.

## Abstract

In this paper, we introduce a potential theory for the k-curvature equation, which can also be seen as a PDE approach to curvature measures. We assign a measure to a bounded, upper semicontinuous function which is strictly subharmonic with respect to the k-curvature operator, and establish the weak continuity of the measure.