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New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Rn

2020-05-13 Education
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Release : 2020-05-13
Genre : Education
Kind : eBook
Book Rating : 616/5 ( reviews)

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Book Synopsis New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Rn by : Antonio Alarcón

Download or read book New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Rn written by Antonio Alarcón. This book was released on 2020-05-13. Available in PDF, EPUB and Kindle. Book excerpt: 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 Rn with any given conformal structure, complete non-orientable minimal surfaces in Rn with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits n hyperplanes of CPn−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 Rn.

New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Mathbb{R}^{n}

2020 Electronic books
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Release : 2020
Genre : Electronic books
Kind : eBook
Book Rating : 126/5 ( reviews)

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Book Synopsis New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Mathbb{R}^{n} by : Antonio Alarcón

Download or read book New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Mathbb{R}^{n} written by Antonio Alarcón. This book was released on 2020. Available in PDF, EPUB and Kindle. Book excerpt: 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 co.

Minimal Surfaces from a Complex Analytic Viewpoint

2021-03-10 Mathematics
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Release : 2021-03-10
Genre : Mathematics
Kind : eBook
Book Rating : 563/5 ( reviews)

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Book Synopsis Minimal Surfaces from a Complex Analytic Viewpoint by : Antonio Alarcón

Download or read book Minimal Surfaces from a Complex Analytic Viewpoint written by Antonio Alarcón. This book was released on 2021-03-10. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann–Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi–Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses.

Global Smooth Solutions for the Inviscid SQG Equation

2020-09-28 Mathematics
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Release : 2020-09-28
Genre : Mathematics
Kind : eBook
Book Rating : 140/5 ( reviews)

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Book Synopsis Global Smooth Solutions for the Inviscid SQG Equation by : Angel Castro

Download or read book Global Smooth Solutions for the Inviscid SQG Equation written by Angel Castro. This book was released on 2020-09-28. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the authors show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.

Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case

2020-09-28 Mathematics
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Release : 2020-09-28
Genre : Mathematics
Kind : eBook
Book Rating : 175/5 ( reviews)

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Book Synopsis Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case by : Jacob Bedrossian

Download or read book Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case written by Jacob Bedrossian. This book was released on 2020-09-28. Available in PDF, EPUB and Kindle. Book excerpt: The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $epsilon leq c_0mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t rightarrow infty $. For times $t gtrsim mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of ``2.5 dimensional'' streamwise-independent solutions referred to as streaks.

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