2019 | The Isoperimetric Inequality: Proofs by Convex and Differential Geometry | Penelope GehringZeitschrift: Rose Hulman Undergraduate Mathematics JournalBand: 20, no. 2Link zur Publikation
The Isoperimetric Inequality: Proofs by Convex and Differential Geometry
Autoren: Penelope Gehring (2019)
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.