Covers, soap films and BV functions

Giovanni Bellettini; Maurizio Paolini; Franco Pasquarelli; Giuseppe Scianna

doi:10.1515/geofl-2018-0005

Covers, soap films and BV functions

Giovanni Bellettini
, Maurizio Paolini
, Franco Pasquarelli
, Giuseppe Scianna

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	57-75
Number of pages	19
Journal	GEOMETRIC FLOWS
Volume	3
DOIs	https://doi.org/10.1515/geofl-2018-0005
Publication status	Published - 2018

Keywords

covering spaces
minimal surfaces
soap films

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10.1515/geofl-2018-0005

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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.",

keywords = "covering spaces, minimal surfaces, soap films, covering spaces, minimal surfaces, soap films",

author = "Giovanni Bellettini and Maurizio Paolini and Franco Pasquarelli and Giuseppe Scianna",

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T1 - Covers, soap films and BV functions

AU - Bellettini, Giovanni

AU - Paolini, Maurizio

AU - Pasquarelli, Franco

AU - Scianna, Giuseppe

PY - 2018

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N2 - 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.

AB - 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.

KW - covering spaces

KW - minimal surfaces

KW - soap films

KW - covering spaces

KW - minimal surfaces

KW - soap films

UR - http://hdl.handle.net/10807/118997

U2 - 10.1515/geofl-2018-0005

DO - 10.1515/geofl-2018-0005

M3 - Article

SN - 2353-3382

VL - 3

SP - 57

EP - 75

JO - GEOMETRIC FLOWS

JF - GEOMETRIC FLOWS

ER -

Covers, soap films and BV functions

Abstract

Keywords

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