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arXiv · 2208.07995

Existence and Stability of $α-$ harmonic Maps

Seyed Mehdi Kazemi Torbaghan·Keyvan Salehi·Salman Babayi
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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 $α-$ 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 from a Riemannian manifold to a Riemannian manifold with non-positive Riemannian curvature is demonstrated. Finally, the instability of $α-$harmonic maps from a compact manifold to a standard unit sphere is investigated.

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Seyed Mehdi Kazemi Torbaghan, Keyvan Salehi, Salman Babayi. 2022-08-16. Existence and Stability of $α-$ harmonic Maps. https://arxiv.org/abs/2208.07995

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