Symplectic Non-hyperbolicity
Symplectic Geometry
2025-04-16 v1 Complex Variables
Differential Geometry
Abstract
Complex (affine) lines are a major object of study in complex geometry, but their symplectic aspects are not well understood. We perform a systematic study based on their associated Ahlfors currents. In particular, we generalize (by a different method) a result of Bangert on the existence of complex lines. We show that Ahlfors currents control the asymptotic behavior of families of pseudoholomorphic curves, refining a result of Demailly. Lastly, we show that the space of Ahlfors currents is convex.
Cite
@article{arxiv.2504.10790,
title = {Symplectic Non-hyperbolicity},
author = {Spencer Cattalani},
journal= {arXiv preprint arXiv:2504.10790},
year = {2025}
}
Comments
22 pages, 4 figures