A Theory of Branched Minimal Surfaces, Anthony Tromba

Автор: Kichoon Yang
Название: Complete Minimal Surfaces of Finite Total Curvature
ISBN: 0792330129 ISBN-13(EAN): 9780792330127
Издательство: Springer
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Описание: Based on the idea that the study of complete minimal surfaces in R3 of finite total curvature amounts to the study of linear series on algebraic curves, this book offers an account of the Puncture Number Problem, which seeks to determine the possible underlying conformal structures for immersed complete minimal surfaces of finite total curvature.

Автор: Giusti
Название: Minimal Surfaces and Functions of Bounded Variation
ISBN: 0817631534 ISBN-13(EAN): 9780817631536
Издательство: Springer
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Описание: The problem of finding minimal surfaces, i. e. of finding the surface of least area among those bounded by a given curve, was one of the first considered after the foundation of the calculus of variations, and is one which received a satis- factory solution only in recent years. Called the problem of Plateau, after the blind physicist who did beautiful experiments with soap films and bubbles, it has resisted the efforts of many mathematicians for more than a century. It was only in the thirties that a solution was given to the problem of Plateau in 3-dimensional Euclidean space, with the papers of Douglas [DJ] and Rado [R T1, 2]. The methods of Douglas and Rado were developed and extended in 3-dimensions by several authors, but none of the results was shown to hold even for minimal hypersurfaces in higher dimension, let alone surfaces of higher dimension and codimension. It was not until thirty years later that the problem of Plateau was successfully attacked in its full generality, by several authors using measure-theoretic methods; in particular see De Giorgi [DG1, 2, 4, 5], Reifenberg [RE], Federer and Fleming [FF] and Almgren [AF1, 2]. Federer and Fleming defined a k-dimensional surface in IR as a k-current, i. e. a continuous linear functional on k-forms. Their method is treated in full detail in the splendid book of Federer [FH 1].

Автор: Nitsche
Название: Lectures on Minimal Surfaces
ISBN: 0521137780 ISBN-13(EAN): 9780521137782
Издательство: Cambridge Academ
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Описание: This 1989 monograph deals with parametric minimal surfaces in Euclidean space. The author presents a broad survey which extends from the classical beginnings to the situation at the time of publication, whilst highlighting many of the subject`s main features and interspersing the mathematical development with pertinent historical remarks.

Автор: Pitts Jon T.
Название: Existence and Regularity of Minimal Surfaces on Riemannian Manifolds. (MN-27):
ISBN: 0691615004 ISBN-13(EAN): 9780691615004
Издательство: Wiley
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Описание: Mathematical No/ex, 27 Originally published in 1981. 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 paper

Автор: Ulrich Dierkes; Albrecht K?ster; Stefan Hildebrand
Название: Regularity of Minimal Surfaces
ISBN: 3642265219 ISBN-13(EAN): 9783642265211
Издательство: Springer
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Описание: This is the second of a three-volume treatise on minimal surfaces. It deals with basic regularity results for minimal surfaces concerning their boundary behavior at Plateau boundaries and free boundaries.

Автор: Ulrich Dierkes; Stefan Hildebrandt; Anthony Tromba
Название: Global Analysis of Minimal Surfaces
ISBN: 3642265332 ISBN-13(EAN): 9783642265334
Издательство: Springer
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Описание: This is the third of a three-volume treatise on minimal surfaces. It deals with geometric properties of minimal surfaces with free boundaries and with a priori gradient estimates for n-dimensional minimal surfaces, leading to various Bernstein-type theorems.

Автор: J.Lucas M. Barbosa; A.Gervasio Colares
Название: Minimal Surfaces in R 3
ISBN: 354016491X ISBN-13(EAN): 9783540164913
Издательство: Springer
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Автор: Ruben Jakob; Ulrich Dierkes; Albrecht K?ster; Stef
Название: Minimal Surfaces
ISBN: 3642265278 ISBN-13(EAN): 9783642265273
Издательство: Springer
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Описание: This is the first of a three-volume treatise on minimal surfaces. It covers the classical theory as well as existence results concerning boundary value problems for minimal surfaces, in particular results for Plateau`s problem.