Asymptotic circularity of immortal area-preserving curvature flows
Asymptotic circularity of immortal area-preserving curvature flows
For a class of area-preserving curvature flows of closed planar curves, we prove that every immortal solution becomes asymptotically circular without any additional assumptions on initial data. As a particular corollary, every solution of zero enclosed area blows up in finite time. This settles an open problem posed by Escher--Ito …