The Global Theory Of Minimal Surfaces In Flat Spaces

Author : W.H. III Meeks,A. Ros,H. Rosenberg
Publisher : Springer
Page : 124 pages
File Size : 54,6 Mb
Release : 2004-10-11
Category : Mathematics
ISBN : 9783540456094

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The Global Theory of Minimal Surfaces in Flat Spaces by W.H. III Meeks,A. Ros,H. Rosenberg Pdf

In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the classical problems were solved and new classes of minimal surfaces found. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry. In this lecture course, Meeks, Ros and Rosenberg, three of the main architects of the modern edifice, present some of the more recent methods and developments of the theory. The topics include moduli, asymptotic geometry and surfaces of constant mean curvature in the hyperbolic space.

Author : Centro Internazionale Matematico Estivo. Session
Publisher : Unknown
Page : 116 pages
File Size : 45,9 Mb
Release : 2002
Category : Electronic
ISBN : OCLC:1132084010

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The Global Theory of Minimal Surfaces in Flat Spaces by Centro Internazionale Matematico Estivo. Session Pdf

Author : William H. III. Meeks,Ros Mulero Ros,Harold Rosenberg,Centro internazionale matematico estivo
Publisher : Unknown
Page : 116 pages
File Size : 51,5 Mb
Release : 2004
Category : Electronic
ISBN : OCLC:803418267

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The Global Theory of Minimal Surfaces in Flat Spaces by William H. III. Meeks,Ros Mulero Ros,Harold Rosenberg,Centro internazionale matematico estivo Pdf

Author : Ulrich Dierkes,Stefan Hildebrandt,Anthony Tromba
Publisher : Springer Science & Business Media
Page : 547 pages
File Size : 52,6 Mb
Release : 2010-08-16
Category : Mathematics
ISBN : 9783642117060

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Global Analysis of Minimal Surfaces by Ulrich Dierkes,Stefan Hildebrandt,Anthony Tromba Pdf

Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise. Part I of the present book can be viewed as an extension of these results. For instance, the first two chapters deal with existence, regularity and uniqueness theorems for minimal surfaces with partially free boundaries. Here one of the main features is the possibility of "edge-crawling" along free parts of the boundary. The third chapter deals with a priori estimates for minimal surfaces in higher dimensions and for minimizers of singular integrals related to the area functional. In particular, far reaching Bernstein theorems are derived. The second part of the book contains what one might justly call a "global theory of minimal surfaces" as envisioned by Smale. First, the Douglas problem is treated anew by using Teichmüller theory. Secondly, various index theorems for minimal theorems are derived, and their consequences for the space of solutions to Plateau ́s problem are discussed. Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented.

Author : William Meeks,Joaquín Pérez
Publisher : American Mathematical Soc.
Page : 195 pages
File Size : 50,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821869123

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A Survey on Classical Minimal Surface Theory by William Meeks,Joaquín Pérez Pdf

Meeks and Pérez extend their 2011 survey article "The classical theory of Minimal surfaces" in the Bulletin of the American Mathematical Society to include other recent research results. Their topics include minimal surfaces with finite topology and more than one end, limits of embedded minimal surfaces without local area or curvature bounds, conformal structure of minimal surfaces, embedded minimal surfaces of finite genus, topological aspects of minimal surfaces, and Calabi-Yau problems. There is no index. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com).

Author : A. T. Fomenko
Publisher : American Mathematical Soc.
Page : 364 pages
File Size : 46,7 Mb
Release : 1993
Category : Minimal surfaces
ISBN : 0821841165

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Minimal Surfaces by A. T. Fomenko Pdf

This book contains recent results from a group focusing on minimal surfaces in the Moscow State University seminar on modern geometrical methods, headed by A. V. Bolsinov, A. T. Fomenko, and V. V. Trofimov. The papers collected here fall into three areas: one-dimensional minimal graphs on Riemannian surfaces and the Steiner problem, two-dimensional minimal surfaces and surfaces of constant mean curvature in three-dimensional Euclidean space, and multidimensional globally minimal and harmonic surfaces in Riemannian manifolds. The volume opens with an exposition of several important problems in the modern theory of minimal surfaces that will be of interest to newcomers to the field. Prepared with attention to clarity and accessibility, these papers will appeal to mathematicians, physicists, and other researchers interested in the application of geometrical methods to specific problems.

Author : Antonio Alarcón,Franc Forstnerič,Francisco J. López
Publisher : Springer Nature
Page : 430 pages
File Size : 54,7 Mb
Release : 2021-03-10
Category : Mathematics
ISBN : 9783030690564

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Minimal Surfaces from a Complex Analytic Viewpoint by Antonio Alarcón,Franc Forstnerič,Francisco J. López Pdf

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.

Author : Robert Osserman
Publisher : Courier Corporation
Page : 224 pages
File Size : 47,8 Mb
Release : 2013-12-10
Category : Mathematics
ISBN : 9780486167695

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A Survey of Minimal Surfaces by Robert Osserman Pdf

Newly updated accessible study covers parametric and non-parametric surfaces, isothermal parameters, Bernstein’s theorem, much more, including such recent developments as new work on Plateau’s problem and on isoperimetric inequalities. Clear, comprehensive examination provides profound insights into crucial area of pure mathematics. 1986 edition. Index.

Author : J. Coates,R. Greenberg,K.A. Ribet,K. Rubin
Publisher : Springer
Page : 269 pages
File Size : 45,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540481607

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Arithmetic Theory of Elliptic Curves by J. Coates,R. Greenberg,K.A. Ribet,K. Rubin Pdf

This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves, and also contain several new results which cannot be found elsewhere in the literature. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.

Author : F. Bethuel,G. Huisken,S. Mueller,K. Steffen
Publisher : Springer
Page : 299 pages
File Size : 42,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540488132

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Calculus of Variations and Geometric Evolution Problems by F. Bethuel,G. Huisken,S. Mueller,K. Steffen Pdf

The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.

Author : N.V. Krylov,M. Röckner,J. Zabczyk
Publisher : Springer
Page : 248 pages
File Size : 40,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540481614

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Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions by N.V. Krylov,M. Röckner,J. Zabczyk Pdf

Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finite-dimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LP-analysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results.

Author : O. Diekmann,R. Durrett,K.-P. Hadeler,P. Maini,H.L. Smith
Publisher : Springer
Page : 274 pages
File Size : 50,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540481706

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Mathematics Inspired by Biology by O. Diekmann,R. Durrett,K.-P. Hadeler,P. Maini,H.L. Smith Pdf

The summer school on Mathematics inspired by Biology was held at Martina Franca, Apulia, Italy in 1997. This volume presents five series of six lectures each. The common theme is the role of structure in shaping transient and ultimate dynamics. But the type of structure ranges from spatial (hadeler and maini in the deterministic setting, Durrett in the stochastic setting) to physiological (Diekmann) and order (Smith). Each contribution sketches the present state of affairs while, by including some wishful thinking, pointing at open problems that deserve attention.

Author : John Erik Fornæss,Marius Irgens,Erlend Fornæss Wold
Publisher : Springer
Page : 309 pages
File Size : 53,5 Mb
Release : 2015-11-05
Category : Mathematics
ISBN : 9783319203379

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Complex Geometry and Dynamics by John Erik Fornæss,Marius Irgens,Erlend Fornæss Wold Pdf

This book focuses on complex geometry and covers highly active topics centered around geometric problems in several complex variables and complex dynamics, written by some of the world’s leading experts in their respective fields. This book features research and expository contributions from the 2013 Abel Symposium, held at the Norwegian University of Science and Technology Trondheim on July 2-5, 2013. The purpose of the symposium was to present the state of the art on the topics, and to discuss future research directions.

Author : Avner Friedman
Publisher : Springer
Page : 210 pages
File Size : 49,7 Mb
Release : 2008-04-26
Category : Mathematics
ISBN : 9783540743316

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Tutorials in Mathematical Biosciences IV by Avner Friedman Pdf

This book offers an introduction to fast growing research areas in evolution of species, population genetics, ecological models, and population dynamics. It reviews the concept and methodologies of phylogenetic trees, introduces ecological models, examines a broad range of ongoing research in population dynamics, and deals with gene frequencies under the action of migration and selection. The book features computational schemes, illustrations, and mathematical theorems.

Author : Antonio Alarcón,Franc Forstnerič,Francisco J. López
Publisher : Unknown
Page : 0 pages
File Size : 49,5 Mb
Release : 2021
Category : Electronic
ISBN : 3030690571

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Minimal Surfaces from a Complex Analytic Viewpoint by Antonio Alarcón,Franc Forstnerič,Francisco J. López Pdf

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.