Horizontal harmonic maps between finsler manifolds

Qun Chen () and Haowei Lin ()
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Qun Chen: Wuhan University
Haowei Lin: Wuhan University

Partial Differential Equations and Applications, 2025, vol. 6, issue 6, 1-22

Abstract: Abstract In this paper, we define the H-energy for maps between Finsler tangent bundles, based on the potential sub-Riemannian structures on the tangent bundles of Finsler manifolds. We introduce a new connection on the Finsler tangent bundle, called HV-connection. Utilizing this connection, we study horizontal harmonic maps between Finsler manifolds, which are critical points under horizontal variations of the H-energy. Under certain additional assumptions, we establish an existence result (Theorem 6.6) of the Dirichlet problem of horizontal harmonic map from compact Finsler manifolds with boundary.

Keywords: Finsler geometry; Harmonic maps; Sub-Laplacian; Sub-Riemannian manifolds; 53C60; 58E20; 35H10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00347-w

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