An inequality for the maximum curvature through a geometric flow

Abstract

We provide a new proof of the following inequality: the maximum curvature $k_{\max }$ and the enclosed area $A$ of a smooth Jordan curve satisfy $k_{\max }\ge \sqrt{\pi /A}$. The feature of our proof is the use of the curve shortening flow.

2 pages

References in corpus (1)

• Mean curvature bounds and eigenvalues of Robin Laplacians

Cited by in corpus (4)

• On the $p$-Laplacian with Robin boundary conditions and boundary trace theorems
• On the isoperimetric inequality for the magnetic Robin Laplacian with negative boundary parameter
• Ramification conjecture and Hirzebruch's property of line arrangements
• Moon in a puddle and the four-vertex theorem