By a length-preserving flow, we provide a new proof of a conjecture on the reverse isoperimetric inequality composed by Pan et al. (Math Inequal Appl 13:329–338, 2010), which states that if $$\gamma $$ γ is a convex curve with length L and enclosed area A , then the best constant $$\varepsilon $$ ε in the inequality $$\begin{aligned} L^2\le 4\pi A+\varepsilon |{\tilde{A}}| \end{aligned}$$ L 2 ≤ 4 π A + ε | A ~ | is $$\pi $$ π , where $${\tilde{A}}$$ A ~ denotes the oriented area of the locus of its curvature centers.

中文翻译：

---

通过保长流的凸平面曲线的逆等周不等式

通过长度保持流，我们为 Pan 等人提出的逆等周不等式的猜想提供了新的证明。(Math Inequal Appl 13:329–338, 2010)，其中指出如果 $$\gamma $$ γ 是长度为 L 且封闭面积为 A 的凸曲线，则不等式中的最佳常数 $$\varepsilon $$ ε $$\begin{aligned} L^2\le 4\pi A+\varepsilon |{\tilde{A}}| \end{对齐}$$ L 2 ≤ 4 π A + ε | 一个~| 是 $$\pi $$ π ，其中 $${\tilde{A}}$$ A ~ 表示其曲率中心轨迹的定向区域。