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arXiv · 1501.03792

An inequality for the maximum curvature through a geometric flow

Konstantin Pankrashkin
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Abstract

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

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Konstantin Pankrashkin. 2015-07-29. An inequality for the maximum curvature through a geometric flow. https://doi.org/10.1007/s00013-015-0804-z

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