On subelliptic harmonic maps with potential

2022/02/13 by Yuxin Dong, Dong, Yuxin, Han Luo +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2202.06346

openalex publication_date 2022/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Let (M,H,g_H;g) be a sub-Riemannian manifold and (N,h) be a Riemannian manifold. For a smooth map u: M → N, we consider the energy functional E_G(u) = (1)/(2) ∫_M[|du_H|²-2G(u)] dV_M, where du_H is the horizontal differential of u, G:N→ ℝ is a smooth function on N. The critical maps of E_G(u) are referred to as subelliptic harmonic maps with potential G. In this paper, we investigate the existence problem for subelliptic harmonic maps with potentials by a subelliptic heat flow. Assuming that the target Riemannian manifold has non-positive sectional curvature and the potential G satisfies various suitable conditions, we prove some Eells-Sampson type existence results when the source manifold is either a step-2 sub-Riemannian manifold or a step-r sub-Riemannian manifold whose sub-Riemannian structure comes from a tense Riemannian foliation.

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