Index of Embedded Networks in the Sphere
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916334373175296 |
|---|---|
| author | Wang, Gaoming |
| author_facet | Wang, Gaoming |
| contents | In this paper, we will compute the Morse index and nullity for the stationary embedded networks in spheres. The key theorem in the computation is that the index (and nullity) for the whole network is related to the index (and nullity) of small networks and the Dirichlet-to-Neumann map defined in this paper. Finally, we will show that for all stationary triple junction networks in $\mathbb{S}^2$, there is only one eigenvalue (without multiplicity) $-1$, which is less than 0, and the corresponding eigenfunctions are locally constant. Besides, the multiplicity of eigenvalues 0 is 3 for these networks, and their eigenfunctions are generated by the rotations on the sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_12653 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Index of Embedded Networks in the Sphere Wang, Gaoming Differential Geometry In this paper, we will compute the Morse index and nullity for the stationary embedded networks in spheres. The key theorem in the computation is that the index (and nullity) for the whole network is related to the index (and nullity) of small networks and the Dirichlet-to-Neumann map defined in this paper. Finally, we will show that for all stationary triple junction networks in $\mathbb{S}^2$, there is only one eigenvalue (without multiplicity) $-1$, which is less than 0, and the corresponding eigenfunctions are locally constant. Besides, the multiplicity of eigenvalues 0 is 3 for these networks, and their eigenfunctions are generated by the rotations on the sphere. |
| title | Index of Embedded Networks in the Sphere |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2110.12653 |