On stability of subelliptic harmonic maps with potential

TL;DR

This paper studies the stability of subelliptic harmonic maps with potential, deriving variation formulas and establishing stability criteria based on curvature and potential Hessian, with applications to maps into spheres.

Contribution

It provides new stability criteria for subelliptic harmonic maps with potential and extends understanding of their behavior in specific target manifolds.

Findings

Stable if target has nonpositive curvature and potential Hessian is nonpositive

Unstable when target is a sphere of dimension ≥ 3

Derived first and second variation formulas for these maps

Abstract

In this paper, we investigate the stability problem of subelliptic harmonic maps with potential. First, we derive the first and second variation formulas for subelliptic harmonic maps with potential. As a result, it is proved that a subelliptic harmonic map with potential is stable if the target manifold has nonpositive curvature and the Hessian of the potential is nonpositive definite. We also give Leung type results which involve the instability of subelliptic harmonic maps with potential when the target manifold is a sphere of dimension $\geq 3$.