Minimal Surfaces In Riemannian Manifolds
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Existence And Regularity Of Minimal Surfaces On Riemannian Manifolds Mn 27
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Author : Jon T. Pitts
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
Existence And Regularity Of Minimal Surfaces On Riemannian Manifolds Mn 27 written by Jon T. Pitts and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
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 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.
Minimal Surfaces In Riemannian Manifolds
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Author : Min Ji
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Minimal Surfaces In Riemannian Manifolds written by Min Ji and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
This monograph studies the structure of the set of all coboundary minimal surfaces in Riemannian manifolds. The authors establish, on a solid analytical foundation, a flexible topological index theory which proves useful for the study of minimal surfaces. One of the highlights of the work is the result that for every Jordan curve on the standard $n$-sphere, there exist at least two minimal surfaces bounded by the curve.
Minimal Surfaces In Riemannian Manifolds
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Author : Min Ji
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Minimal Surfaces In Riemannian Manifolds written by Min Ji and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
A multiple solution theory to the Plateau problem in a Riemannian manifold is established. In [italic capital]S[superscript italic]n, the existence of two solutions to this problem is obtained. The Morse-Tompkins-Shiffman Theorem is extended to the case when the ambient space admits no minimal sphere.
Introduction To Global Analysis Minimal Surfaces In Riemannian Manifolds
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Author : John Douglas Moore
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-12-15
Introduction To Global Analysis Minimal Surfaces In Riemannian Manifolds written by John Douglas Moore and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-15 with Electronic books categories.
During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold determine the homology of the manifold. Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs. This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed parametrized minimal surfaces in a compact Riemannian manifold, establishing Morse inequalities for perturbed versions of the energy function on the mapping space. It studies the bubbling which occurs when the perturbation is turned off, together with applications to the existence of closed minimal surfaces. The Morse-Sard theorem is used to develop transversality theory for both closed geodesics and closed minimal surfaces. This book is based on lecture notes for graduate courses on “Topics in Differential Geometry”, taught by the author over several years. The reader is assumed to have taken basic graduate courses in differential geometry and algebraic topology.
Existence And Regularity Of Minimal Surfaces On Riemannian Manifolds
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Author : Jon T. Pitts
language : en
Publisher:
Release Date : 1981
Existence And Regularity Of Minimal Surfaces On Riemannian Manifolds written by Jon T. Pitts and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Minimal Surfaces In Riemannian Manifolds
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Author : Min Ji
language : en
Publisher: Oxford University Press, USA
Release Date : 2014-08-31
Minimal Surfaces In Riemannian Manifolds written by Min Ji and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-31 with MATHEMATICS categories.
This monograph studies the structure of the set of all coboundary minimal surfaces in Riemannian manifolds. The authors establish, on a solid analytical foundation, a flexible topological index theory which proves useful for the study of minimal surfaces. One of the highlights of the work is the result that for every Jordan curve on the standard $n$-sphere, there exist at least two minimal surfaces bounded by the curve.
Minimal Surfaces
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Author : A. T. Fomenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Minimal Surfaces written by A. T. Fomenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Minimal surfaces categories.
This book contains recent results from a group focusing on minimal surfaces in the Moscow State University seminar on modern geometrical methods, headed by A. V. Bolsinov, A. T. Fomenko, and V. V. Trofimov. The papers collected here fall into three areas: one-dimensional minimal graphs on Riemannian surfaces and the Steiner problem, two-dimensional minimal surfaces and surfaces of constant mean curvature in three-dimensional Euclidean space, and multidimensional globally minimal and harmonic surfaces in Riemannian manifolds. The volume opens with an exposition of several important problems in the modern theory of minimal surfaces that will be of interest to newcomers to the field. Prepared with attention to clarity and accessibility, these papers will appeal to mathematicians, physicists, and other researchers interested in the application of geometrical methods to specific problems.
Regularity Of Minimal Surfaces
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Author : Ulrich Dierkes
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-16
Regularity Of Minimal Surfaces 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 2010-08-16 with Mathematics categories.
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.
Lectures On Minimal Submanifolds
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Author : H. Blaine Lawson
language : en
Publisher:
Release Date : 1980
Lectures On Minimal Submanifolds written by H. Blaine Lawson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
A Survey Of Minimal Surfaces
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Author : Robert Osserman
language : en
Publisher: Courier Corporation
Release Date : 1986-01-01
A Survey Of Minimal Surfaces written by Robert Osserman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-01-01 with Mathematics categories.
This clear and comprehensive study features 12 sections that discuss parametric and non-parametric surfaces, surfaces that minimize area, isothermal parameters, Bernstein's theorem, minimal surfaces with boundary, and many other topics. This revised edition includes material on minimal surfaces in relativity and topology and updated work on Plateau's problem and isoperimetric inequalities. 1969 edition.