Topics in Geometric Analysis

Heiko von der Mosel

(RWTH Aachen)

On integral Menger curvature

Using concepts from elementary geometry like the circumcircle radius one can construct various families of geometric curvature energies quite useful in harmonic analysis and geometric knot theory. After surveying these results I will report on recent progress on a gradient flow for integral Menger curvature.

Lynn Heller

(Universität Hannover)

Area Estimates for High genus Lawson surfaces via DPW

Starting at a saddle tower surface, we give a new existence proof of the Lawson surfaces \(\xi_{m,k}\) of high genus by deforming the corresponding DPW potential. As a byproduct, we obtain for fixed \(m\) estimates on the area of \(\xi_{m,k} \) in terms of their genus \(g= mk >>1\).