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.
Bellettini, G., Paolini, M., Pasquarelli, F., Scianna, G. (2018). Covers, soap films and BV functions. GEOMETRIC FLOWS, 3(1), 57-75 [10.1515/geofl-2018-0005].
Covers, soap films and BV functions
BELLETTINI, GIOVANNI;SCIANNA, GIUSEPPE
2018-01-01
Abstract
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.
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https://hdl.handle.net/11365/1019577