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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Geometry and Topology Seminar: Characterizing non-positive curvature via an isoperimetric inequality.

Presented by Stefan Wenger., Fribourg.

4 February 2016 13:00 in CM221.

The aim of this talk is to show that a locally compact geodesic metric
space has non-positive curvature in the sense of Alexandrov (i.e. is a
CAT(0)-space) if and only if it admits a quadratic isoperimetric
inequality for curves with sharp Euclidean constant, that is, if every
closed curve of length $l$ bounds a disc of area at most $(4\pi)^{-1} l^2$.

The proof of this result is based on (1) a solution of the classical
problem of Plateau in the general setting of proper metric spaces and
(2) properties of the intrinsic structure of minimal discs in metric
spaces. Based on joint work with A. Lytchak.

Contact mark.a.powell@durham.ac.uk or andrew.lobb@durham.ac.uk or wilhelm.klingenberg@durham.ac.uk for more information