Sturm theory, Ghys theorem on zeroes of the Schwarzian derivative and flattening of Legendrian curves
V. Ovsienko (CNRS, Luminy--Marseille FRANCE), S. Tabachnikov, (University of Arkansas Fayetteville, USA, MPI Bonn, Germany)
TL;DR
This paper explores the relationship between Ghys' theorem on the zeros of the Schwarzian derivative, flattening points of Legendrian curves, and Sturm theory, providing insights into their interconnected geometric and analytical properties.
Contribution
It establishes a connection between Ghys' theorem, flattening points of Legendrian curves, and Sturm theory, offering new perspectives on their interplay.
Findings
Ghys' theorem on four zeros of the Schwarzian derivative is analyzed.
The relation between flattening points of Legendrian curves and Sturm theory is elucidated.
New insights into the geometric implications of the Schwarzian derivative zeros are provided.
Abstract
We discuss Ghys' theorem on 4 zeroes of the Schwarzian derivative and its relation with flattening points of Legendrian curves and Sturm theory.
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Taxonomy
TopicsMeromorphic and Entire Functions · Algebraic Geometry and Number Theory · Analytic and geometric function theory