Steiner's formula and a variational proof of the isoperimetric inequality
Differential Geometry
2021-01-15 v3 Classical Analysis and ODEs
Abstract
We give a new proof of the isoperimetric inequality in the plane, based on Steiner's formula for the area of a convex neighborhood. This proof establishes the isoperimetric inequality directly, without requiring that we separately establish the existence of an optimal domain. In doing so, this proof bypasses the main difficulty in all of the proofs Steiner outlined for the plane isoperimetric inequality.
Keywords
Cite
@article{arxiv.1909.06347,
title = {Steiner's formula and a variational proof of the isoperimetric inequality},
author = {Joseph Ansel Hoisington},
journal= {arXiv preprint arXiv:1909.06347},
year = {2021}
}
Comments
Comments Welcome! v3 contains a new proof of one of the main lemmas, and a correspondingly simplified proof of the main result. The proof of the characterization of equality in this version also addresses a gap in this part of the proof in v1 and v2