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

Risultato della ricerca: Contributo in rivista › Articolo in rivista › 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.

Lingua originale	English
pagine (da-a)	57-75
Numero di pagine	19
Rivista	GEOMETRIC FLOWS
Volume	3
DOI	https://doi.org/10.1515/geofl-2018-0005
Stato di pubblicazione	Pubblicato - 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.",

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

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AU - Bellettini, Giovanni

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AU - Pasquarelli, Franco

AU - Scianna, Giuseppe

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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

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JO - GEOMETRIC FLOWS

JF - GEOMETRIC FLOWS

ER -

Covers, soap films and BV functions

Abstract

Keywords

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Altri file e collegamenti

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