Regularity of minimal surfaces
Regularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and bou...
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| Auteurs principaux: | , , |
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| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Édition: | Revised and enlarged 2nd edition. |
| Collection: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
340 Grundlehren der mathematischen Wissenschaften 340 |
| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Edition revue et augmentée avec la participation de Anthony J. Tromba 1ère édition publiée en 1992 chez Springer dans la même collection : volumes 295 et 296 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Regularity of minimal surfaces, Ulrich Dierkes, Stefan Hildebrandt and Anthony J. Tromba, Revised and enlarged 2nd edition, 2010, Heidelberg, Springer, 1 vol. (XVII-623 p.), Grundlehren der mathematischen Wissenschaften, 978-3-642-11699-5 |
| Résumé: | Regularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general Gauss-Bonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is that, for principal reasons, it is impossible to derive a priori estimates. Therefore regularity proofs for non-minimizers have to be based on indirect reasoning using monotonicity formulas. This is followed by a long chapter discussing geometric properties of minimal and H-surfaces such as enclosure theorems and isoperimetric inequalities, leading to the discussion of obstacle problems and of Plateau s problem for H-surfaces in a Riemannian manifold. A natural generalization of the isoperimetric problem is the so-called thread problem, dealing with minimal surfaces whose boundary consists of a fixed arc of given length. Existence and regularity of solutions are discussed. The final chapter on branch points presents a new approach to the theorem that area minimizing solutions of Plateau s problem have no interior branch points |
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| Description: | Edition revue et augmentée avec la participation de Anthony J. Tromba 1ère édition publiée en 1992 chez Springer dans la même collection : volumes 295 et 296 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliographie: | Bibliogr. Index |
| ISBN: | 9783642117008 |
| ISSN: | 0072-7830 |
| Accès: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |