07.06.2018 17:15 Ulrich Pinkall (TU Berlin) :
A Weierstrass representation for 2D elasticity MI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

We study a class of elastic energy functionals for maps between planar domains (among them the so-called squared distance functional) whose critical points (elastic maps) allow a far more complete theory than one would expect from general elasticity theory. For some of these functionals elastic maps even admit a "Weierstrass representation" in terms of holomorphic functions, reminiscent of the one for minimal surfaces. We also prove a global uniqueness theorem that does not seem to be known in other situations.