Anisotropic area-preserving flows for plane curves and entropy inequalities

This paper describes two anisotropic area-preserving flows for plane curves, both of which are considered to deform one convex curve into another.Different monotonic entropy functions are identified under these flows, which can be utilized to derive two significant entropy inequalities: the log-Minkowski inequality and the curvature entropy inequality, as well as the Brunn-Minkowski inequality.