Flowing to minimal surfaces
Presenting author: Melanie Rupflin
We discuss the construction and properties of a gradient flow that is designed to change surfaces in arbitrary targets into critical points of the Area functional, i.e. into minimal immersions. As we shall explain, the study of this flow requires a precise understanding of so called horizontal curves of metrics on hyperbolic surfaces and the developed theory has applications also in other parts of geometric analysis such as the study of eigenvalues of the Laplacian on hyperbolic surfaces.