The Isoperimetric Inequality: Proofs by Convex and Differential Geometry

Authors

Penelope Gehring, Potsdam UniversityFollow

Abstract

The Isoperimetric Inequality has many different proofs using methods from diverse mathematical fields. In the paper, two methods to prove this inequality will be shown and compared. First the 2-dimensional case will be proven by tools of elementary differential geometry and Fourier analysis. Afterwards the theory of convex geometry will briefly be introduced and will be used to prove the Brunn--Minkowski-Inequality. Using this inequality, the Isoperimetric Inquality in n dimensions will be shown.

Author Bio

Penelope Gehring completed this work on July the 12th of 2017 at the Eberhard Karls University at Tübingen. This work is the bachelor thesis she handed in to receive her bachelor degree in mathematics in summer 2017. Now she is a student in the international master program of mathematical physics at Tübingen. She wants to expand her knowledge in differential geometry and mathematical relativity, so she wants to start as a doctoral student in these field after her graduation.

Faculty Sponsor

Carla Cederbaum

Recommended Citation

Gehring, Penelope (2019) "The Isoperimetric Inequality: Proofs by Convex and Differential Geometry," Rose-Hulman Undergraduate Mathematics Journal: Vol. 20: Iss. 2, Article 4.
Available at: https://scholar.rose-hulman.edu/rhumj/vol20/iss2/4