Shrinkers of the area-preserving curve-shortening flow: Existence and saddle-point property

Nikita Cernomazov

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arXiv · 2508.00352

Shrinkers of the area-preserving curve-shortening flow: Existence and saddle-point property

Nikita Cernomazov

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Abstract

We consider homothetic evolutions of the area-preserving curve-shortening flow (APCSF), that is, classical curve shortening flow with an additional non-local forcing term. By using known results on $\lambda$-curves, we prove the existence of non-circular shrinkers for this flow. In our first main result, we present a partial classification scheme, similar to the well-known Abresch-Langer classification for shrinkers of curve-shortening flow. Finally, we also deduce a saddle-point property for all non-circular (APCSF)-shrinkers analogous to the known saddle-point property of Abresch-Langer curves.

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BibTeX RIS

Nikita Cernomazov. 2025-08-01. Shrinkers of the area-preserving curve-shortening flow: Existence and saddle-point property. https://arxiv.org/abs/2508.00352

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