On a General Linear Nonlocal Curvature Flow of Convex Plane Curves

Motivated by Pan-Yang [PY] and Ma-Cheng [MC], we study a general linear nonlocal curvature flow for convex closed plane curves and discuss the short time existence and asymptotic convergence behavior of the flow. Due to the linear structure of the flow, this partial differential equation problem can be resolved using an ordinary differential equation method, together with the help of representation formula for solutions to a linear heat equation.