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Existence and Stability of α−Harmonic Maps

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  • Seyed Mehdi Kazemi Torbaghan
  • Keyvan Salehi
  • Salman Babayi

Abstract

In this paper, we first study the α−energy functional, Euler‐Lagrange operator, and α‐stress‐energy tensor. Second, it is shown that the critical points of the α−energy functional are explicitly related to harmonic maps through conformal deformation. In addition, an α−harmonic map is constructed from any smooth map between Riemannian manifolds under certain assumptions. Next, we determine the conditions under which the fibers of horizontally conformal α−harmonic maps are minimal submanifolds. Then, the stability of any α−harmonic map on Riemannian manifold with nonpositive curvature is studied. Finally, the instability of α−harmonic maps from a compact manifold to a standard unit sphere is investigated.

Suggested Citation

  • Seyed Mehdi Kazemi Torbaghan & Keyvan Salehi & Salman Babayi, 2022. "Existence and Stability of α−Harmonic Maps," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:1906905
    DOI: 10.1155/2022/1906905
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    References listed on IDEAS

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    1. Ahmad Sulaiman Ahmad El-Faqeer & Zhen Chuan Ng & Shamani Supramaniam & V. Ravichandran, 2021. "On Convolution and Convex Combination of Harmonic Mappings," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, August.
    2. Seyed Mehdi Kazemi Torbaghan & Keyvan Salehi & Salman Babayi & Rafael López, 2022. "Existence and Stability of α−Harmonic Maps," Journal of Mathematics, Hindawi, vol. 2022, pages 1-10, October.
    3. Seyed Mehdi Kazemi Torbaghan & Keyvan Salehi & Salman Babayi, 2022. "Existence and Stability of α−Harmonic Maps," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    4. Mengkun Zhu & Xinzhong Huang, 2015. "The Distortion Theorems for Harmonic Mappings with Analytic Parts Convex or Starlike Functions of Order," Journal of Mathematics, Hindawi, vol. 2015, pages 1-6, October.
    5. S. Hansraj & K. S. Govinder & N. Mewalal, 2013. "Conformal Mappings in Relativistic Astrophysics," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-12, July.
    6. S. Hansraj & K. S. Govinder & N. Mewalal, 2013. "Conformal Mappings in Relativistic Astrophysics," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
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    1. Seyed Mehdi Kazemi Torbaghan & Keyvan Salehi & Salman Babayi, 2022. "Existence and Stability of α−Harmonic Maps," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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