A note on the existence of nontrivial zero modes on Riemannian manifolds
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909848751308800 |
|---|---|
| author | Reuß, Jonah |
| author_facet | Reuß, Jonah |
| contents | We prove a necessary criterion for the (non-)existence of nontrivial solutions to the Dirac equation $Dψ=i A \cdot_{Cl} ψ$ on Riemannian manifolds that are either closed or of bounded geometry. This generalizes a result of Rupert Frank and Michael Loss on $\mathbb{R}^n$ where the criterion relates the $L^n$-norm of $A$ to the Sobolev constant on $\mathbb{R}^n$. On Riemannian manifolds the role of the Sobolev constant will be replaced by the Yamabe invariant. If $n$ is odd, we show that our criterion is sharp on $\mathbb{S}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01602 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the existence of nontrivial zero modes on Riemannian manifolds Reuß, Jonah Differential Geometry 53C37 (Primary) 34L40, 53C18 (Secondary) We prove a necessary criterion for the (non-)existence of nontrivial solutions to the Dirac equation $Dψ=i A \cdot_{Cl} ψ$ on Riemannian manifolds that are either closed or of bounded geometry. This generalizes a result of Rupert Frank and Michael Loss on $\mathbb{R}^n$ where the criterion relates the $L^n$-norm of $A$ to the Sobolev constant on $\mathbb{R}^n$. On Riemannian manifolds the role of the Sobolev constant will be replaced by the Yamabe invariant. If $n$ is odd, we show that our criterion is sharp on $\mathbb{S}^n$. |
| title | A note on the existence of nontrivial zero modes on Riemannian manifolds |
| topic | Differential Geometry 53C37 (Primary) 34L40, 53C18 (Secondary) |
| url | https://arxiv.org/abs/2503.01602 |