在這篇論文中，我們介紹何謂"凸集最適長度假說"以及定義一個曲線的"最適長度簡介"，探討平面上任意凸集以及任意給定面積的最適長度以及滿足最適長度的曲線應該有那些性質，並找出一些種類的曲線可以滿足 "凸集分割的最適長度假說"。
我們成功的論證，任何橢圓"最適長度簡介"必定小於同面積下的圓的"最適長度簡介"。並且，我們萃取出橢圓的其中一個重要性質，那就是完全四對稱性質，並且我們也成功證明所有完全四對稱性質的封閉平滑曲線依然滿足這個假說。
最後，我們使用變分法，試著說明圓形的最適長度簡介在面積不變的擾動下，有區域最大值。並且，我們用"曲線縮短流"理論說明，如果存在一個違反此假說的曲線存在，會發生什麼事情以及此曲線的性質。

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.

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