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Horizontal harmonic maps between finsler manifolds

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  • Qun Chen

    (Wuhan University)

  • Haowei Lin

    (Wuhan University)

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.

Suggested Citation

  • Qun Chen & Haowei Lin, 2025. "Horizontal harmonic maps between finsler manifolds," Partial Differential Equations and Applications, Springer, vol. 6(6), pages 1-22, December.
    • Handle: RePEc:spr:pardea:v:6:y:2025:i:6:d:10.1007_s42985-025-00347-w
    DOI: 10.1007/s42985-025-00347-w
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