Year: 2026
Type: preprint
Abstract: We construct a closed surface of genus $2$ with nonpositive Gaussian curvature and a complete nonperiodic flat geodesic asymptotic to a flat closed geodesic. The metric is of class $C^{3,1/3}$ and its curvature is of class $C^{1,1/3}$, but not $C^2$. Thus the periodic-asymptote obstruction for smooth surfaces does not extend to $C^1$ Gaussian curvature.
Source: arXiv (Cornell University)
Author: Qiu, Hongda
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223276387