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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}
}
R2 v1 2026-06-22T20:23:49.491Z