# The geometry of constant mean curvature surfaces in Euclidean space

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Giuseppe Tinaglia

created by raffero on 14 Apr 2021

modified on 28 Apr 2021

19 may 2021
-- 11:00

Differential Geometry Seminar Torino (online)

**Abstract.**

I will begin by reviewing classical geometric properties of constant mean curvature surfaces, $H>0$, in $\mathbb{R}^3$. I will then talk about several more recent results for surfaces embedded in $\mathbb{R}^3$ with constant mean curvature, such as curvature and radius estimates. I will show applications of such estimates including a characterisation of the round sphere as the only simply-connected surface embedded in $\mathbb{R}^3$ with constant mean curvature and area estimates for compact surfaces embedded in a flat torus with constant mean curvature and finite genus. I will also talk about the geometry of compact hyper surfaces embedded in a manifold with constant mean curvature and finite index.

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The link of the virtual room will be sent one day before the talk to all registered participants. To register, please send an e-mail to dgseminar.torino@gmail.com