Abstract :

Main aim of this talk is to present a fairly elementary proof of the classical Isoperimetric Inequality, which is precisely as follows: $$ | \partial \Omega |_{N-1} \geq N \omega^{\frac{1}{N}}_N |\Omega|^{1-\frac{1}{N}} $$ where $\Omega$ is a smooth domain in $\mathbb{R}^N$ and $|.|_{N-1}, |.|$ are $(N-1)$ dimensional surface measure and Lebesgue measure respectively and $\omega$ is the volume of unit ball in $\mathbb{R}^N$. We will be using some simple ideas of PDE and Alexandrov's moving plane method.