Lectures On Minimal Surfaces Introduction Fundamentals Geometry And Basic Boundary Value Problems
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Lectures On Minimal Surfaces
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Author : Johannes C. C. Nitsche
language : en
Publisher:
Release Date : 1989
Lectures On Minimal Surfaces written by Johannes C. C. Nitsche and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
Lectures On Minimal Surfaces Introduction Fundamentals Geometry And Basic Boundary Value Problems
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Author : Johannes C. C. Nitsche
language : en
Publisher:
Release Date : 1989
Lectures On Minimal Surfaces Introduction Fundamentals Geometry And Basic Boundary Value Problems written by Johannes C. C. Nitsche and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
This book is a revised and translated version of the first five chapters of Vorlesungen ^D"uber Minimalfl^D"achen. It deals with the parametric minimal surface in Euclidean space. The author presents a broad survey that extends from the classical beginnings to the current situation while highlighting many of the subject's main features and interspersing the mathematical development with pertinent historical remarks.
A Course In Minimal Surfaces
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Author : Tobias Holck Colding
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-18
A Course In Minimal Surfaces written by Tobias Holck Colding and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-18 with Mathematics categories.
Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces. This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science. The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle.
Minimal Surfaces I
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Author : Ulrich Dierkes
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Minimal Surfaces I written by Ulrich Dierkes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
Minimal surfaces I is an introduction to the field of minimal surfaces and apresentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can alsobe useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory fornonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.
Foliations And The Geometry Of 3 Manifolds
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Author : Danny Calegari
language : en
Publisher: Clarendon Press
Release Date : 2007-05-17
Foliations And The Geometry Of 3 Manifolds written by Danny Calegari and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-17 with Mathematics categories.
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in 1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Computer Algebra In Scientific Computing
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Author : Andreas Weber
language : en
Publisher: MDPI
Release Date : 2019-11-04
Computer Algebra In Scientific Computing written by Andreas Weber and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-04 with Computers categories.
Although scientific computing is very often associated with numeric computations, the use of computer algebra methods in scientific computing has obtained considerable attention in the last two decades. Computer algebra methods are especially suitable for parametric analysis of the key properties of systems arising in scientific computing. The expression-based computational answers generally provided by these methods are very appealing as they directly relate properties to parameters and speed up testing and tuning of mathematical models through all their possible behaviors. This book contains 8 original research articles dealing with a broad range of topics, ranging from algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic over the integers and rational numbers over methods for certifying the isolated zeros of polynomial systems to computer algebra problems in quantum computing.
From Riemann To Differential Geometry And Relativity
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Author : Lizhen Ji
language : en
Publisher: Springer
Release Date : 2017-10-03
From Riemann To Differential Geometry And Relativity written by Lizhen Ji and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-03 with Mathematics categories.
This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.
The Theory Of Quantum Torus Knots Volume Iii
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Author : Michael Ungs
language : en
Publisher: Lulu.com
Release Date : 2010-08-16
The Theory Of Quantum Torus Knots Volume Iii written by Michael Ungs and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-16 with Technology & Engineering categories.
Appendicies A to I that are referenced by Volumes I and II in the theory of quantum torus knots (QTK). A detailed mathematical derivation of space curves is provided that links the diverse fields of superfluids, quantum mechanics, and hydrodynamics.
Geometry V
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Author : Robert Osserman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Geometry V written by Robert Osserman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Few people outside of mathematics are aware of the varieties of mathemat ical experience - the degree to which different mathematical subjects have different and distinctive flavors, often attractive to some mathematicians and repellant to others. The particular flavor of the subject of minimal surfaces seems to lie in a combination of the concreteness of the objects being studied, their origin and relation to the physical world, and the way they lie at the intersection of so many different parts of mathematics. In the past fifteen years a new component has been added: the availability of computer graphics to provide illustrations that are both mathematically instructive and esthetically pleas ing. During the course of the twentieth century, two major thrusts have played a seminal role in the evolution of minimal surface theory. The first is the work on the Plateau Problem, whose initial phase culminated in the solution for which Jesse Douglas was awarded one of the first two Fields Medals in 1936. (The other Fields Medal that year went to Lars V. Ahlfors for his contributions to complex analysis, including his important new insights in Nevanlinna Theory.) The second was the innovative approach to partial differential equations by Serge Bernstein, which led to the celebrated Bernstein's Theorem, stating that the only solution to the minimal surface equation over the whole plane is the trivial solution: a linear function.