Loewner's "forgotten" theorem

Peter Albers; Serge Tabachnikov

doi:10.1007/s00283-021-10144-z

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arXiv · 2109.03051

Loewner's "forgotten" theorem

Peter Albers·Serge Tabachnikov

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Abstract

Let $f(t)$ be a smooth and periodic function of one real variable. Then the planar curves $t\mapsto \big(f'(t),f(t)\big)$ and $t\mapsto \big(f''(t)-f(t),f'(t)\big)$ both have non-negative rotation number around every point not on the curve. These are the two simplest cases of a beautiful Theorem by C. Loewner. This article is expository, we prove the two statements by elementary means following work by Bol [3]. After that, we present Loewner's Theorem and his proof from [7].

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BibTeX RIS

Peter Albers, Serge Tabachnikov. 2021-09-07. Loewner's "forgotten" theorem. https://doi.org/10.1007/s00283-021-10144-z

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