Abstract: Weierstrass-type representations allow the analytic construction of surfaces from holomorphic data. The surfaces obtained in this way are often characterised by a constant curvature property, e.g., minimal surfaces in Euclidean space, maximal surfaces in Lorentzian space or i-minimal surfaces in isotropic space.

In discrete differential geometry, where nets are considered instead of smooth surfaces, discrete counterparts of these surface classes can be defined via a discrete notion of curvature based on Steiner’s formula. Discrete Weierstrass representations have been shown to exist for most of these discrete nets. In this talk, we will explore the setup of discrete curvature line nets in Laguerre geometry and show that the discrete Weierstrass-type representations in Euclidean, Lorentzian and isotropic space are instances of the same geometric construction.

Der Link zum Vortrag findet sich auf der Website unter https://www.vsmath.at/academics/phd-colloquia/.