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New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in $/mathbb {R}^n$ (Paperback) Loot Price: R2,215
Discovery Miles 22 150
New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in $/mathbb {R}^n$ (Paperback): Antonio Alarcon,...

New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in $/mathbb {R}^n$ (Paperback)

Antonio Alarcon, Franc Forstneric, Francisco J Lopez

Series: Memoirs of the American Mathematical Society

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Loot Price R2,215 Discovery Miles 22 150 | Repayment Terms: R208 pm x 12*

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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 $\mathbb{R}^n$.

General

Imprint: American Mathematical Society
Country of origin: United States
Series: Memoirs of the American Mathematical Society
Release date: October 2020
Authors: Antonio Alarcon • Franc Forstneric • Francisco J Lopez
Dimensions: 254 x 178mm (L x W)
Format: Paperback
Pages: 77
ISBN-13: 978-1-4704-4161-6
Categories: Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
Books > Science & Mathematics > Mathematics > Geometry > General
Books > Science & Mathematics > Mathematics > Topology > General
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LSN: 1-4704-4161-6
Barcode: 9781470441616

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