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New Complex Analytic Methods in the Study of Non-orientable Minimal Surfaces in Mathbb Rn - Couverture souple

Alarcon, Antonio; Forstneric, Franc; Lopez, Francisco J.

 
9781470441616: New Complex Analytic Methods in the Study of Non-orientable Minimal Surfaces in Mathbb Rn
Couverture souple
ISBN 10 : 1470441616 ISBN 13 : 9781470441616
Editeur : American Mathematical Society, 2020

Synopsis

The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable conformal minimal surfaces in $\mathbb{R}^n$ for any $n\ge 3$. These methods, which the authors develop essentially from the first principles, enable them to prove that the space of conformal minimal immersions of a given bordered non-orientable surface to $\mathbb{R}^n$ is a real analytic Banach manifold, obtain approximation results of Runge-Mergelyan type for conformal minimal immersions from non-orientable surfaces, and show general position theorems for non-orientable conformal minimal surfaces in $\mathbb{R}^n$. The authors also give the first known example of a properly embedded non-orientable minimal surface in $\mathbb{R}^4$; a Mobius strip.

All the new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice of a conformal structure. This enables the authors to obtain significant new applications to the global theory of non-orientable minimal surfaces. In particular, they construct proper non-orientable conformal minimal surfaces in $\mathbb{R}^n$ with any given conformal structure, complete non-orientable minimal surfaces in $\mathbb{R}^n$ with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits $n$ hyperplanes of $\mathbb{CP}^{n-1}$ in general position, complete non-orientable minimal surfaces bounded by Jordan curves, and complete proper non-orientable minimal surfaces normalized by bordered surfaces in $p$-convex domains of $\mathbb{R}^n$.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

Antonio Alarcon, Universidad de Granada, Spain.

Franc Forstneric, University of Ljubljana, Slovenia.

Francisco J. Lopez, Universidad de Granada, Spain.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2020
Langue
anglais
ISBN 10 
1470441616
ISBN 13 
9781470441616
Reliure
Broché
Nombre de pages
77
Coordonnées du fabricant
non disponible
Personne responsable
non disponible