Weil-Petersson curves and finite total curvature (Christopher Bishop, Stony Brook University)

02.12.2019 17:30 – 18:30

In 2006 Takhtajan and Teo defined a Weil-Petersson metric making universal Teichmuller space (essentially the space of planar quasicircles) into a disconnected Hilbert manifold. The Weil-Petersson class is the unique connected component containing all smooth curves, and consists of certain rectifiable quasicircles. There are several known function theoretic characterizations of WP curves, including connections to Loewner's equation and SLE. In this lecture, I will describe some new geometric characterizations that say a quasicircle is WP iff some measure of local curvature is square integrable over all locations and scales. Here local curvature can be measured using quantities such as: beta-numbers, Menger curvature, integral geometry, inscribed polygons, tangent directions, and associated convex hulls and minimal surfaces in hyperbolic 3-space.

Lieu

Room 17, Att. unusual time, Séminaire "Mathématique Physique"

entrée libre