Some works on "Convex Body Isoperimetric Problem"

Abstract

The goal of this paper is to study some properties about the isoperimetric profile of convex bodies in the plane find some conditions that make the conjecture true and give some types of curves that the convex body isoperimetric conjecture holds on them We have verified any ellipses satisfies the conjecture Moreover we discover a kind of important properties from ellipse called completely 4-symmetric and we also check that the convex body isoperimetric conjecture remains true on any smooth completely 4-symmetric curves We verify that the isoperimetric profile of a unit ball B has a local maximum for all available area under the area-preserving variation on B Finally we try to relate curve-shortening flow and convex body isoperimetric conjecture that is we discover some properties about smooth convex curves that breaks the conjecture by using relate curve-shortening flow

Date of Award	2020
Original language	English
Supervisor	Ye-Kai Wang (Supervisor)