Antonio Alarcon, Franc Forstneric, Francisco J. Lopez New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in $\mathbb {R}^n$ 9781470441616

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Автор: Antonio Alarcon, Franc Forstneric, Francisco J. Lopez
Название: New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in $\mathbb {R}^n$
ISBN: 9781470441616
Издательство: Mare Nostrum (Eurospan)
Классификация:

Основы высшей математики и математический анализ

Геометрия

Топология

ISBN-10: 1470441616
Обложка/Формат: Paperback
Страницы: 77
Вес: 0.19 кг.
Дата издания: 30.06.2020
Серия: Memoirs of the american mathematical society
Язык: English
Размер: 254 x 178
Ключевые слова: Calculus & mathematical analysis,Geometry,Topology
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Поставляется из: Англии
Описание: 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 $\mathbb{R}^n$.
Дополнительное описание: Calculus and mathematical analysis|Geometry|Topology

New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in $\mathbb {R}^n$, Antonio Alarcon, Franc Forstneric, Francisco J. Lopez