Year: 2026
Type: preprint
Abstract: We prove that a complete surface of finite topological type satisfying Condition A is homeomorphic to the two-torus. More generally, we show that an isolated planar end of a complete open surface satisfying Condition A cannot be periodic under the induced action on the space of ends. Condition A includes dense periodic points, a uniformly hyperbolic splitting into one-dimensional subbundles for a complete metric, and invariant line fields that uniquely integrate to transverse stable and unstable foliations. These results give a partial answer to the question of whether a complete surface satisfying Condition A must be compact.
Source: arXiv (Cornell University)
Authors: Ures, Raúl, Yu, Tongyao
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213520590