arXiv subjects

Ivan Krznarić

Publications and source records attributed to Ivan Krznarić.

2 recordsLinked to original sources

arXiv2026

The inverse curve shortening flow on the hyperbolic plane

We study the inverse curve shortening flow in the hyperbolic plane $\h^2$. We classify all solitons with respect to parabolic and conformal vector fields of $\h^2$. In the upper half-plane model of $\h^2$, we prove that parabolic solitons are all graphs on the $y$-axis, whereas conformal solitons are graphs on the $x$-axis. We study the concavity of these solitons and when they approach the coordinate axes.

math.DG↗

arXiv2026

Geometric aspects of the curve shortening flow in the hyperbolic plane

We define a new notion of translations in the hyperbolic plane and explicitly solve the equation of the curve shortening flow. Next, we consider the class of ancient convex solutions and solve the equation of the curve shortening flow when the curvature function is given by separation of variables. Lastly, we prove some area estimates for closed ancient solutions of the curve shortening flow.

math.DG↗