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Author: Katsuei Kenmotsu
Publisher: American Mathematical Soc.
ISBN: 9780821834794
Category : Mathematics
Languages : en
Pages : 156
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Book Description
The mean curvature of a surface is an extrinsic parameter measuring how the surface is curved in the three-dimensional space. A surface whose mean curvature is zero at each point is a minimal surface, and it is known that such surfaces are models for soap film. There is a rich and well-known theory of minimal surfaces. A surface whose mean curvature is constant but nonzero is obtained when we try to minimize the area of a closed surface without changing the volume it encloses. An easy example of a surface of constant mean curvature is the sphere. A nontrivial example is provided by the constant curvature torus, whose discovery in 1984 gave a powerful incentive for studying such surfaces. Later, many examples of constant mean curvature surfaces were discovered using various methods of analysis, differential geometry, and differential equations. It is now becoming clear that there is a rich theory of surfaces of constant mean curvature. In this book, the author presents numerous examples of constant mean curvature surfaces and techniques for studying them. Many finely rendered figures illustrate the results and allow the reader to visualize and better understand these beautiful objects. The book is suitable for advanced undergraduates, graduate students and research mathematicians interested in analysis and differential geometry.
Author: Katsuei Kenmotsu
Publisher: American Mathematical Soc.
ISBN: 9780821834794
Category : Mathematics
Languages : en
Pages : 156
Get Book Here
Book Description
The mean curvature of a surface is an extrinsic parameter measuring how the surface is curved in the three-dimensional space. A surface whose mean curvature is zero at each point is a minimal surface, and it is known that such surfaces are models for soap film. There is a rich and well-known theory of minimal surfaces. A surface whose mean curvature is constant but nonzero is obtained when we try to minimize the area of a closed surface without changing the volume it encloses. An easy example of a surface of constant mean curvature is the sphere. A nontrivial example is provided by the constant curvature torus, whose discovery in 1984 gave a powerful incentive for studying such surfaces. Later, many examples of constant mean curvature surfaces were discovered using various methods of analysis, differential geometry, and differential equations. It is now becoming clear that there is a rich theory of surfaces of constant mean curvature. In this book, the author presents numerous examples of constant mean curvature surfaces and techniques for studying them. Many finely rendered figures illustrate the results and allow the reader to visualize and better understand these beautiful objects. The book is suitable for advanced undergraduates, graduate students and research mathematicians interested in analysis and differential geometry.
Author: Eamon Barrett
Publisher:
ISBN:
Category : Curves on surfaces
Languages : en
Pages : 230
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Book Description
Author: Daniel J. Weser
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We study the qualitative and quantitative properties of sets with boundaries of almost-constant mean curvature. For open subsets of Rn+1, we will prove L2- quantitative stability estimates in the presence of bubbling. In the case of droplets adhering to a substrate, we will classify their shapes in the small mass regime and prove a compactness theorem for droplets with boundaries of almost-constant mean curvature and almost-constant angle of contact with the substrate
Author: Bennett Palmer
Publisher:
ISBN:
Category :
Languages : en
Pages : 156
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Book Description
Author: Lawrence E. Schmidt
Publisher:
ISBN:
Category : Surfaces
Languages : en
Pages : 24
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Book Description
Author: David Dudley Bleecker
Publisher:
ISBN:
Category :
Languages : en
Pages : 144
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Book Description
Author: Rafael López
Publisher: Springer Science & Business Media
ISBN: 3642396267
Category : Mathematics
Languages : en
Pages : 296
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Book Description
The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical fields. While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of “compact surfaces with boundaries,” narrowing its focus to a geometric view. Basic issues include the discussion whether the symmetries of the curve inherit to the surface; the possible values of the mean curvature, area and volume; stability; the circular boundary case and the existence of the Plateau problem in the non-parametric case. The exposition provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambient spaces. Throughout the text, numerous illustrations clarify the results and their proofs. The book is intended for graduate students and researchers in the field of differential geometry and especially theory of surfaces, including geometric analysis and geometric PDEs. It guides readers up to the state-of-the-art of the theory and introduces them to interesting open problems.
Author: D. Hoffmann
Publisher:
ISBN:
Category : Surfaces of constant curvature
Languages : en
Pages : 56
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Book Description
Author: Giuseppe Buttazzo
Publisher: Walter de Gruyter
ISBN: 3110870479
Category : Mathematics
Languages : en
Pages : 229
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Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author: Kenneth A. Brakke
Publisher: Princeton University Press
ISBN: 1400867436
Category : Mathematics
Languages : en
Pages : 258
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Book Description
Kenneth Brakke studies in general dimensions a dynamic system of surfaces of no inertial mass driven by the force of surface tension and opposed by a frictional force proportional to velocity. He formulates his study in terms of varifold surfaces and uses the methods of geometric measure theory to develop a mathematical description of the motion of a surface by its mean curvature. This mathematical description encompasses, among other subtleties, those of changing geometries and instantaneous mass losses. Originally published in 1978. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
