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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in $/mathbb {R}^n$ (Paperback)
Loot Price: R2,343
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New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in $/mathbb {R}^n$ (Paperback)
Series: Memoirs of the American Mathematical Society
Expected to ship within 12 - 17 working days
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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 $\mathbb{R}^n$.
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