A curvature flow in the plane with a nonlocal term (Q1751567)

The authors study the geometric flow of a planar curve driven by its curvature and the normal derivative of its capacity potential. The paper contains five sections. Sections 1 and 2 contains preliminary results. In Section 3, the authors have used a combination between a time-shift technique and geometric comparison to prove some of the main results of this paper. The last two sections are dedicated also to the proof of the main results. More precisely, in Section 5, the authors give the proof of the most important theorem from this paper, namely Theorem 1.1.