Vorträge in der Woche 26.06.2017 bis 02.07.2017

Dienstag, 27.06.2017: Cuspidal types and Characters

Steven Charlton

Dienstag, 27.06.2017: Deformation of metrics towards constant scalar curvature

Prof. Dr. Simon Brendle (Columbia University)

The classical uniformization theorem asserts that any Riemannian metric on a closed two- dimensional surface is conformal to a metric of constant Gaussian curvature. A higher dimensio- nal analogue of this statement is given by the solution of the Yamabe problem: Any metric on an n-dimensional manifold is conformal to a metric of constant scalar curvature. This problem is equivalent to the existence of a positive solution of the nonlinear elliptic equation of the form $\Delta u - \frac{n-2}{4(n-1)} R u + c u^{\frac{n+2}{n-2}} = 0$. In this lectures, I will describe the background of this problem, and its variational formulation in terms of the Yamabe functional. The gradient flow associated with the Yamabe functional leads to an curvature flow, and I will discuss why this flow converges to a metric of constant scalar curvature for any initial metric.

Donnerstag, 29.06.2017: The Fingerprints of Black Holes - Shadows and their Degeneracies

Claudio Paganini (Albert-Einstein-Institut Golm)

First I will introduce the concept of the shadow of a black hole and what it means for the shadows of two observers to be degenerate. I will then present preliminary results showing that no continuous degenerations exist between the shadows of observers at any point in the DOC of any Kerr-Newman-(anti)- De-Sitter black hole spacetime of unit mass. Therefore an observer can, by measuring the black holes shadow, in principle determine the angular momentum, the charge and the cosmological constant of the black hole under observation, as well as his radial distance from the black hole and his angle of elevation above the equatorial plane.

Donnerstag, 29.06.2017: "Endlichdimensionale Approximation des Koopmanoperators

Tim Krake

Donnerstag, 29.06.2017: On Existence of Static Metric Extensions alà Miao

Annachiara Piubello (Universität Tübingen)

We analyze the static metric extension conjecture proposed by Bartnik and studied by P. Miao. This is motivated by problems related to quasi-local mass in General Relativity. We show that there exists an asymptotically flat and scalar flat static extension of the metric on the outside space of a ball of constant radius R such that it satisfies Bartnik's geometric boundary condition if we start with a metric which is a slightly modification of the Euclidean one and that has reflection invariant boundary data.