Geometry Workshop Obergurgl 2021

Abstract: An immersion f :M ->R³ of a surface M is called constrained Willmore if f minimizes the Willmore functional W(f) compared to local variations of f that change the induced metric only conformally. We present a version of this variational problem in the context of Discrete Differential Geometry and use it to develop an efficient numerical algorithm. This algorithm allows us to experimentally explore the possible shapes of Willmore minimizers within a given conformal class.