A heat equation on a quaternionic contact manifold

TL;DR

This paper introduces a heat equation specific to quaternionic contact manifolds and demonstrates that its associated energy functional decreases over time under certain positivity conditions.

Contribution

It defines a new quaternionic contact heat equation and proves the monotonicity of its energy functional on compact manifolds.

Findings

Energy functional is monotone non-increasing under the qc heat flow

Monotonicity holds under specific positivity conditions

Provides a new analytical tool for quaternionic contact geometry

Abstract

A quaternionic contact (qc) heat equation and the corresponding qc energy functional are introduced. It is shown that the qc energy functional is monotone non-increasing along the qc heat equation on a compact qc manifold provided certain positivity conditions are satisfied.