Official Summary of Security Transactions and Holdings Reported to the Securities and Exchange Commission Under the Securities Exchange Act of 1934 and the Public Utility Holding Company Act of 1935 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Official Summary of Security Transactions and Holdings Reported to the Securities and Exchange Commission Under the Securities Exchange Act of 1934 and the Public Utility Holding Company Act of 1935 write by United States. Securities and Exchange Commission. This book was released on 1998. Official Summary of Security Transactions and Holdings Reported to the Securities and Exchange Commission Under the Securities Exchange Act of 1934 and the Public Utility Holding Company Act of 1935 available in PDF, EPUB and Kindle.
A Survey on Classical Minimal Surface Theory
A Survey on Classical Minimal Surface Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Survey on Classical Minimal Surface Theory write by William Meeks. This book was released on 2012. A Survey on Classical Minimal Surface Theory available in PDF, EPUB and Kindle. 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).
A Survey of Minimal Surfaces
A Survey of Minimal Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Survey of Minimal Surfaces write by Robert Osserman. This book was released on 2002. A Survey of Minimal Surfaces available in PDF, EPUB and Kindle.
Regularity of Minimal Surfaces
Regularity of Minimal Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Regularity of Minimal Surfaces write by Ulrich Dierkes. This book was released on 2010-08-16. Regularity of Minimal Surfaces available in PDF, EPUB and Kindle. Regularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general Gauss-Bonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is that, for principal reasons, it is impossible to derive a priori estimates. Therefore regularity proofs for non-minimizers have to be based on indirect reasoning using monotonicity formulas. This is followed by a long chapter discussing geometric properties of minimal and H-surfaces such as enclosure theorems and isoperimetric inequalities, leading to the discussion of obstacle problems and of Plateau ́s problem for H-surfaces in a Riemannian manifold. A natural generalization of the isoperimetric problem is the so-called thread problem, dealing with minimal surfaces whose boundary consists of a fixed arc of given length. Existence and regularity of solutions are discussed. The final chapter on branch points presents a new approach to the theorem that area minimizing solutions of Plateau ́s problem have no interior branch points.
Minimal Surfaces
Minimal Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Minimal Surfaces write by Ulrich Dierkes. This book was released on 2010-08-16. Minimal Surfaces available in PDF, EPUB and Kindle. Minimal Surfaces is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339-341). Each volume can be read and studied independently of the others. The central theme is boundary value problems for minimal surfaces. The treatise is a substantially revised and extended version of the monograph Minimal Surfaces I, II (Grundlehren Nr. 295 & 296). The first volume begins with an exposition of basic ideas of the theory of surfaces in three-dimensional Euclidean space, followed by an introduction of minimal surfaces as stationary points of area, or equivalently, as surfaces of zero mean curvature. The final definition of a minimal surface is that of a nonconstant harmonic mapping X: \Omega\to\R^3 which is conformally parametrized on \Omega\subset\R^2 and may have branch points. Thereafter the classical theory of minimal surfaces is surveyed, comprising many examples, a treatment of Björling ́s initial value problem, reflection principles, a formula of the second variation of area, the theorems of Bernstein, Heinz, Osserman, and Fujimoto. The second part of this volume begins with a survey of Plateau ́s problem and of some of its modifications. One of the main features is a new, completely elementary proof of the fact that area A and Dirichlet integral D have the same infimum in the class C(G) of admissible surfaces spanning a prescribed contour G. This leads to a new, simplified solution of the simultaneous problem of minimizing A and D in C(G), as well as to new proofs of the mapping theorems of Riemann and Korn-Lichtenstein, and to a new solution of the simultaneous Douglas problem for A and D where G consists of several closed components. Then basic facts of stable minimal surfaces are derived; this is done in the context of stable H-surfaces (i.e. of stable surfaces of prescribed mean curvature H), especially of cmc-surfaces (H = const), and leads to curvature estimates for stable, immersed cmc-surfaces and to Nitsche ́s uniqueness theorem and Tomi ́s finiteness result. In addition, a theory of unstable solutions of Plateau ́s problems is developed which is based on Courant ́s mountain pass lemma. Furthermore, Dirichlet ́s problem for nonparametric H-surfaces is solved, using the solution of Plateau ́s problem for H-surfaces and the pertinent estimates.
