# Convexity of level sets and a two-point function

## TL;DR

This paper introduces a maximum principle for a two-point function to analyze the convexity of level sets of harmonic functions, leading to a strict convexity result related to principal curvature.

## Contribution

It develops a novel maximum principle for two-point functions to study convexity properties of harmonic function level sets.

## Key findings

- Proves a maximum principle for a two-point function.
- Establishes strict convexity of level sets based on principal curvature.
- Links convexity of level sets to harmonic functions' geometric properties.

## Abstract

We establish a maximum principle for a two-point function in order to analyze the convexity of level sets of harmonic functions. We show that this can be used to prove a strict convexity result involving the smallest principal curvature of the level sets.