New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in $\mathbb {R}^n$ (Memoirs of the American Mathematical Society)
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 $\mathbb{R}^n$.
Yazar | Franc Forstneric (author) & Francisco J. Lopez (author) Antonio Alarcon (author) |
---|---|
Yayın Evi | American Mathematical Society |
Fransızca Independently published İngilizce İspanyolca ROBERT H BORK MDPI AG WADE H MCCREE Springer HACHETTE LIVRE-BNF Kolektif Book on Demand Ltd. Gale, U.S. Supreme Court Records Almanca ERWIN N GRISWOLD Rusça Additional Contributors Türkçe LAP LAMBERT Academic Publishing
indir okumak internet üzerinden
Baskı Detayları
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 |
Son kitaplar
İlgili kitaplar
Research in Collegiate Mathematics Education IV (CBMS ISSUES IN MATHEMATICS EDUCATION): v. 4
indir bedava
Groups and Computation II (DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE): v. 2
indir bedava
Amplitudes, Hodge Theory and Ramification: From Periods an Motives to Feynman Amplitudes: 2014 Clay Mathematics Institute Summer School Periods and ... 2014 (Clay Mathematics Proceedings, Band 21)
indir bedava
Davenport-Zannier Polynomials and Dessins dEnfants (Mathematical Surveys and Monographs, Band 249)
indir bedava
Research in Collegiate Mathematics Education IV (CBMS ISSUES IN MATHEMATICS EDUCATION): v. 4
indir bedava
Groups and Computation II (DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE): v. 2
indir bedava
Amplitudes, Hodge Theory and Ramification: From Periods an Motives to Feynman Amplitudes: 2014 Clay Mathematics Institute Summer School Periods and ... 2014 (Clay Mathematics Proceedings, Band 21)
indir bedava
Davenport-Zannier Polynomials and Dessins dEnfants (Mathematical Surveys and Monographs, Band 249)
indir bedava