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.

Bellettini, G., Paolini, M., Pasquarelli, F., Scianna, G., Covers, soap films and BV functions, <<GEOMETRIC FLOWS>>, 2018; 3 (1): 57-75. [doi:10.1515/geofl-2018-0005] [http://hdl.handle.net/10807/118997]

Covers, soap films and BV functions

Bellettini, Giovanni;Paolini, Maurizio;Pasquarelli, Franco;
2018

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.
Inglese
Bellettini, G., Paolini, M., Pasquarelli, F., Scianna, G., Covers, soap films and BV functions, <<GEOMETRIC FLOWS>>, 2018; 3 (1): 57-75. [doi:10.1515/geofl-2018-0005] [http://hdl.handle.net/10807/118997]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/118997
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