Contactomorphic vertically convex domains
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912837392138240 |
|---|---|
| author | Eyll, Jan Fritsch, Jonas Zehmisch, Kai |
| author_facet | Eyll, Jan Fritsch, Jonas Zehmisch, Kai |
| contents | We consider the standard Darboux space equipped with the radial symmetric contact form. We study co-orientation preserving contactomorphisms between relatively compact domains up to the boundary. We determine the contactomorphism classes among all strict vertically convex domains over a round ball in the Liouville hyperplane that are radially symmetric about the Reeb axis and whose boundary coincide along a neighbourhood of the common equator. The total invariant is the mean curvature of the bounding sphere at the umbilic points with the same sign. Replacing the Liouville hyperplane by codisc bundles of closed non-Besse Riemannian manifolds or finite symplectisations of closed non-Besse strict contact manifolds analogous results are formulated in terms of characteristic length and total characteristic action, resp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14842 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Contactomorphic vertically convex domains Eyll, Jan Fritsch, Jonas Zehmisch, Kai Symplectic Geometry 53D35, 53D05, 37C27, 37J55, 57R17 We consider the standard Darboux space equipped with the radial symmetric contact form. We study co-orientation preserving contactomorphisms between relatively compact domains up to the boundary. We determine the contactomorphism classes among all strict vertically convex domains over a round ball in the Liouville hyperplane that are radially symmetric about the Reeb axis and whose boundary coincide along a neighbourhood of the common equator. The total invariant is the mean curvature of the bounding sphere at the umbilic points with the same sign. Replacing the Liouville hyperplane by codisc bundles of closed non-Besse Riemannian manifolds or finite symplectisations of closed non-Besse strict contact manifolds analogous results are formulated in terms of characteristic length and total characteristic action, resp. |
| title | Contactomorphic vertically convex domains |
| topic | Symplectic Geometry 53D35, 53D05, 37C27, 37J55, 57R17 |
| url | https://arxiv.org/abs/2601.14842 |