Franc Forstneric (author) & Francisco J. Lopez (author) Antonio Alarcon (author) New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in $\mathbb {R}^n$ (Memoirs of the American Mathematical Society) internet üzerinden ibook

New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in $\mathbb {R}^n$ (Memoirs of the American Mathematical Society)

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Springer ERWIN N GRISWOLD Independently published Book on Demand Ltd. Additional Contributors Gale, U.S. Supreme Court Records İngilizce HACHETTE LIVRE-BNF MDPI AG İspanyolca ROBERT H BORK WADE H MCCREE Türkçe Fransızca LAP LAMBERT Academic Publishing Almanca Kolektif Rusça
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Yazar Franc Forstneric (author) & Francisco J. Lopez (author) Antonio Alarcon (author)
İsbn 10 1470441616
İsbn 13 978-1470441616
Yayın Evi American Mathematical Society
tarafından gönderildi New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in $\mathbb {R}^n$ (Memoirs of the American Mathematical Society) 30 Mart 2020

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 $\mathbb{R}^n$.

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