https://neckpinch.com/authors/nikita-cernomazov/New arXiv papers by Nikita Cernomazov, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2508.00352/arxiv:2508.00352Fri, 01 Aug 2025 00:00:00 GMTNikita Cernomazov — 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 λ-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.Curve shorteningVolume-preserving & constrained flowsRicci solitons