Covers, soap films and BV functions

In this paper we review the double covers method with constrained BV functions for solving the classical Plateau’s problem. Next, we carefully analyze some interesting examples of soap films compatible with covers of degree larger than two: in particular, the case of a soap film only partially wetti...

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Veröffentlicht in:	Geometric flows 2018-03, Vol.3 (1), p.57-75
Hauptverfasser:	Bellettini, Giovanni, Paolini, Maurizio, Pasquarelli, Franco, Scianna, Giuseppe
Format:	Artikel
Sprache:	eng
Schlagworte:	49Q05 (minimal surfaces) 49Q15 (geometric measure and integration theory) 57M10 (covering spaces)
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Zusammenfassung:	In this paper we review the double covers method with constrained BV functions for solving the classical Plateau’s problem. Next, we carefully analyze some interesting examples of soap films compatible with covers of degree larger than two: 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, a soap film that retracts to its boundary, and various soap films spanning an octahedral frame.
ISSN:	2353-3382 2353-3382
DOI:	10.1515/geofl-2018-0005