The Geometry of Constant Mean Curvature Surfaces in Euclidean Space
Time: 2016-10-25
Published By: Ningbo Lu
Speaker(s): Giuseppe Tinaglia( King's College London)
Time: 10:00-11:00 August 29, 2016
Venue: Room 29, Quan Zhai, BICMR
Abstract: In this talk I will begin by reviewing classical geometric properties of constant mean curvature surfaces, H>0, in R^3. I will then talk about several more recent results for surfaces embedded in R^3 with constant mean curvature, such as curvature and radius estimates for simply-connected surfaces embedded in R^3 with constant mean curvature. Finally I will show applications of such estimates including a characterisation of the round sphere as the only simply-connected surface embedded in R^3 with constant mean curvature and area estimates for compact surfaces embedded in a flat torus with constant mean curvature and finite genus. This is joint work with Meeks.