A Weierstrass representation for 2D elasticity
Differential Geometry
2017-06-21 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1706.06387,
title = {A Weierstrass representation for 2D elasticity},
author = {Ulrich Pinkall and Jonas Tervooren},
journal= {arXiv preprint arXiv:1706.06387},
year = {2017}
}