Title: A fourth order parabolic curvature flow for the isoperimetric problem

Speaker: James McCoy (University of Newcastle)

Time：2024年11月18日，15:00-16：00

Place: Management Building, Room 1308

Abstract: We consider closed, embedded, planar curves evolving by a fourth order curvature flow under which the enclosed area is nondecreasing while the length is nonincreasing.  We show that initial curves of sufficiently small oscillation of curvature converge exponentially in the $C^\infty$-topology to circles.  Consequently this flow may be used to prove the isoperimetric inequality for such curves that, in particular, need not be convex nor starshaped.  This is joint work with Yong Wei and Glen Wheeler.