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arXiv · 2605.13023

Geometric aspects of the curve shortening flow in the hyperbolic plane

Ivan Krznarić·Rafael López
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Abstract

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.

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Ivan Krznarić, Rafael López. 2026-05-13. Geometric aspects of the curve shortening flow in the hyperbolic plane. https://arxiv.org/abs/2605.13023

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