Year: 2026
Type: preprint
Abstract: We study the solitons of the inverse curve shortening flow in the hyperbolic plane with respect to Killing fields: all parabolic fields, and the hyperbolic and elliptic fields with unit translation length and unit angular speed. The three cases reduce to one planar system. Except for a family of horocycles, every soliton has an endpoint at finite distance where the curvature blows up and the curve is a branch of a cusp. In the parabolic and elliptic cases there is a critical value $H$ of the parameter of the family: below $H$ the other end meets the ideal boundary orthogonally, above $H$ it is a second singular endpoint, and at $H$ the curvature tends to $1$. In the hyperbolic case $H=π/2$ and the critical solitons are horocycles. These horocycles are the only complete solitons and the only solitons of constant curvature.
Source: arXiv (Cornell University)
Authors: Krznarić, Ivan, López, Rafael
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161290727