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The Stability of $\alpha-$ Harmonic Maps with Physical Applications

Differential Geometry 2022-08-26 v1 Mathematical Physics math.MP

Abstract

The first result in this study is a non-existence theorem for α\alpha-harmonic mappings. Additionally, a direct connection between the α\alpha- harmonic and harmonic maps is made possible via conformal deformation. Second, the instability of non-constant α\alpha-harmonic maps is investigated with regard to the target manifold's Ricci curvature requirements. Next, the concept of α\alpha-stable manifolds and their physical applications are explored. Finally, it is investigated the α\alpha-stability of compact Riemannian manifolds that admit a non-isometric conformal vector field as well as the Einstein Riemannian manifolds under certain assumption on the smallest positive eigenvalue of its Laplacian operator on functions.

Keywords

Cite

@article{arxiv.2208.11817,
  title  = {The Stability of $\alpha-$ Harmonic Maps with Physical Applications},
  author = {Seyed Mehdi Kazemi Torbaghan and Keyvan Salehi},
  journal= {arXiv preprint arXiv:2208.11817},
  year   = {2022}
}