A contractible Schiffer counterexample on the half-sphere
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912632639848448 |
|---|---|
| author | Cao-Labora, Gonzalo Fernández, Antonio J. |
| author_facet | Cao-Labora, Gonzalo Fernández, Antonio J. |
| contents | We show the existence of a family of nontrivial smooth contractible domains on the sphere that admit Neumann eigenfunctions of the Laplacian which are constant on the boundary. These domains are contained on the half-sphere, in stark contrast with the rigidity literature for Serrin-type problems. The proof relies on a local bifurcation argument around the family of geodesic disks centered at the north pole. We combine the use of anisotropic Hölder spaces for the functional setting with computer-assisted techniques to check the bifurcation conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05732 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A contractible Schiffer counterexample on the half-sphere Cao-Labora, Gonzalo Fernández, Antonio J. Analysis of PDEs Differential Geometry We show the existence of a family of nontrivial smooth contractible domains on the sphere that admit Neumann eigenfunctions of the Laplacian which are constant on the boundary. These domains are contained on the half-sphere, in stark contrast with the rigidity literature for Serrin-type problems. The proof relies on a local bifurcation argument around the family of geodesic disks centered at the north pole. We combine the use of anisotropic Hölder spaces for the functional setting with computer-assisted techniques to check the bifurcation conditions. |
| title | A contractible Schiffer counterexample on the half-sphere |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2510.05732 |