arXiv subjects

Jan Eyll

Publications and source records attributed to Jan Eyll.

2 recordsLinked to original sources

arXiv2026

Contactomorphic vertically convex domains

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.

math.SG↗

arXiv2025

Stability of systolic inequalities for the M\"obius strip and Klein bottle

The systolic area $\alpha_{sys}$ of a nonsimply connected compact Riemannian surface $(M,g)$ is defined as its area divided by the square of the systole, where the systole is equal to the length of a shortest noncontractible closed curve. The systolic inequality due to Bavard states that on the Klein bottle, the systolic area has the optimal lower bound $\frac{2\sqrt{2}}{\pi}$. Bavard also constructed metrics of minimal systolic area in any given conformal class. We give an alternative proof of these results, which also yields an estimate on the systolic defect $\alpha_{sys}-\frac{2\sqrt{2}}{\pi}$ in terms of the $L^2$-distance of the conformal factor to the metric which minimizes the systolic area. On the M\"obius strip, we also prove similar estimates for metrics in fixed conformal classes.

math.DG↗