Jürgen Klenk

Existence of stationary vacuum solutions of Einstein's equations in an exterior domain

A proof is given for the existence and uniqueness of a stationary vacuum solution (.<#, g, £) of the boundary value problem consisting of Einsteins equations in an exterior domain ^ diffeomorphic lol x £ (where £ = (R 3 \B(0, /?)) and boundary data depending on the Killing field f on 3E. The boundary data must be sufficiently close to that of a stationary, spatially conformally fiat vacuum solution (JZ, J, |) .

Modeling Knowledge and Reasoning using Locally Active Elements in Semantic Networks

A model for knowledge and reasoning based on self-organizing semantic networks is presented. The self-organization is driven by locally active elements in the network, which allows to model the cognitive process of understanding as an iteration of classification and segmentation, both of which are particular locally active elements. Applications to Natural Language Understanding are indicated.

Geometric properties of rotating stars in general relativity

We prove precise a priori estimates from above for the equatorial radius, the mass and the angular momentum of a rotating star in general relativity, provided that the star is stationary and axisymmetric with perfect fluid matter satisfying the dominant energy condition and possesses an equatorial plane which is stable in the sense of minimal surfaces.