On stability of exponentially subelliptic harmonic maps

TL;DR

This paper investigates the stability of exponentially subelliptic harmonic maps from sub-Riemannian to Riemannian manifolds, deriving variation formulas and establishing stability or instability depending on the target's curvature.

Contribution

It derives the first and second variation formulas for these harmonic maps and characterizes their stability based on the curvature of the target manifold.

Findings

Stable when the target has nonpositive curvature

Unstable when the target is a sphere

Provides explicit variation formulas

Abstract

In this paper, we study the stability problem of exponentially subelliptic harmonic maps from sub-Riemannian manifolds to Riemannian manifolds. We derive the rst and second variation formulas for exponentially subelliptic harmonic maps, and apply these formulas to prove that if the target manifold has nonpositive curvature, the exponentially subelliptic harmonic map is stable. Further, we obtain the instability of exponentially subelliptic harmonic maps when the target manifold is a sphere.