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Author | : Kichoon Yang |
Publisher | : Springer Science & Business Media |
Total Pages | : 167 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401711046 |
Download Complete Minimal Surfaces of Finite Total Curvature Book in PDF, ePub and Kindle
This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature. Our exposition is based upon the philosophy that the study of finite total curvature complete minimal surfaces in R3, in large measure, coincides with the study of meromorphic functions and linear series on compact Riemann sur faces. This philosophy is first indicated in the fundamental theorem of Chern and Osserman: A complete minimal surface M immersed in R3 is of finite total curvature if and only if M with its induced conformal structure is conformally equivalent to a compact Riemann surface Mg punctured at a finite set E of points and the tangential Gauss map extends to a holomorphic map Mg _ P2. Thus a finite total curvature complete minimal surface in R3 gives rise to a plane algebraic curve. Let Mg denote a fixed but otherwise arbitrary compact Riemann surface of genus g. A positive integer r is called a puncture number for Mg if Mg can be conformally immersed into R3 as a complete finite total curvature minimal surface with exactly r punctures; the set of all puncture numbers for Mg is denoted by P (M ). For example, Jorge and Meeks [JM] showed, by constructing an example g for each r, that every positive integer r is a puncture number for the Riemann surface pl.
Author | : Yi Fang |
Publisher | : |
Total Pages | : 154 |
Release | : 1990 |
Genre | : Gauss maps |
ISBN | : |
Download Complete Minimal Surfaces of Finite Total Curvature Book in PDF, ePub and Kindle
Author | : Robert Osserman |
Publisher | : Courier Corporation |
Total Pages | : 224 |
Release | : 2013-12-10 |
Genre | : Mathematics |
ISBN | : 0486167690 |
Download A Survey of Minimal Surfaces Book in PDF, ePub and Kindle
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 | : W.H. III Meeks |
Publisher | : Springer |
Total Pages | : 124 |
Release | : 2004-10-11 |
Genre | : Mathematics |
ISBN | : 3540456090 |
Download The Global Theory of Minimal Surfaces in Flat Spaces Book in PDF, ePub and Kindle
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 | : Kichoon Yang |
Publisher | : Springer Science & Business Media |
Total Pages | : 185 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9400910150 |
Download Complete and Compact Minimal Surfaces Book in PDF, ePub and Kindle
'Et moi ..., si j'avait su comment en reveni.r, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non 111e series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Author | : David Hoffman |
Publisher | : |
Total Pages | : 89 |
Release | : 1995 |
Genre | : |
ISBN | : |
Download Complete embedded minimal surfaces of finite total curvature Book in PDF, ePub and Kindle
Author | : Robert Osserman |
Publisher | : Springer Science & Business Media |
Total Pages | : 279 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 3662034840 |
Download Geometry V Book in PDF, ePub and Kindle
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.
Author | : Antonio Alarcón |
Publisher | : Springer Nature |
Total Pages | : 430 |
Release | : 2021-03-10 |
Genre | : Mathematics |
ISBN | : 3030690563 |
Download Minimal Surfaces from a Complex Analytic Viewpoint Book in PDF, ePub and Kindle
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 | : A. T. Fomenko |
Publisher | : American Mathematical Soc. |
Total Pages | : 156 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821837915 |
Download Elements of the geometry and topology of minimal surfaces in three-dimensional space Book in PDF, ePub and Kindle
This book grew out of lectures presented to students of mathematics, physics, and mechanics by A. T. Fomenko at Moscow University, under the auspices of the Moscow Mathematical Society. The book describes modern and visual aspects of the theory of minimal, two-dimensional surfaces in three-dimensional space. The main topics covered are: topological properties of minimal surfaces, stable and unstable minimal films, classical examples, the Morse-Smale index of minimal two-surfaces in Euclidean space, and minimal films in Lobachevskian space. Requiring only a standard first-year calculus and elementary notions of geometry, this book brings the reader rapidly into this fascinating branch of modern geometry.
Author | : Seong-Deog Yang |
Publisher | : |
Total Pages | : 122 |
Release | : 1997 |
Genre | : |
ISBN | : |
Download On a Connected Sum Construction for Complete Minimal Surfaces of Finite Total Curvature Book in PDF, ePub and Kindle