Covers, soap films and BV functions
Differential Geometry
2017-10-12 v2
Abstract
In this paper we first review the covering space method with constrained BV functions for solving the classical Plateau's problem. Next, we carefully analyze some interesting examples of soap films compatible with the covering space method: in particular, the case of a soap film only partially wetting a space curve, a soap film spanning a cubical frame but having a large tunnel, aa soap film that retracts onto its boundary, hence not modelable with the Reifenberg method, and various soap films spanning an octahedral frame.
Cite
@article{arxiv.1710.01606,
title = {Covers, soap films and BV functions},
author = {Giovanni Bellettini and Maurizio Paolini and Franco Pasquarelli and Giuseppe Scianna},
journal= {arXiv preprint arXiv:1710.01606},
year = {2017}
}