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Loewner curvature

Friday 19th June 2015 - 11:30 to 12:30
INI Seminar Room 1
Co-author: Steffen Rohde (University of Washington)

Inspired by the geometric understanding of the SLE trace, there has been interest in studying how the deterministic Loewner equation encodes geometric properties of 2-dim sets into the 1-dim data of the driving function. Working in this vein, we define a new notion of curvature, called Loewner curvature, so-named because it captures key behavior of the trace curve of the Loewner equation. The Loewner curvature is defined for (nice enough) curves that begin at a marked boundary point of a Jordan domain and grow towards a second marked boundary point. We show that if this curvature is small, then the curve must remain a simple curve.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons