论文标题
$α-$谐波图与物理应用的稳定性
The Stability of $α-$ Harmonic Maps with Physical Applications
论文作者
论文摘要
这项研究的第一个结果是$α-$谐波映射的不存在定理。此外，通过共形变形使$α-$谐波和谐波图之间的直接连接成为可能。其次，根据目标歧管的RICCI曲率要求，研究了非恒定$α$ harmonic地图的不稳定性。接下来，探索了$α-$稳定流形的概念及其物理应用。最后，正在研究紧凑的riemannian歧管的$α-$稳定性，该歧管接纳了非等级保形矢量场以及在其Laplacian操作员功能的最小正征值的某些假设下，在某些假设下，Einstein Riemannian歧管。
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.
