The Stability of α- Harmonic Maps with Physical Applications
Abstract
The first result in this study is a non-existence theorem for α-harmonic mappings. Additionally, a direct connection between the α- harmonic and harmonic maps is made possible via conformal deformation. Second, the instability of non-constant α-harmonic maps is investigated with regard to the target manifold's Ricci curvature requirements. Next, the concept of α-stable manifolds and their physical applications are explored. Finally, it is investigated the α-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.
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