Constant Mean Curvature Surfaces With Boundary

DOWNLOAD

Download Constant Mean Curvature Surfaces With Boundary PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Constant Mean Curvature Surfaces With Boundary book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Constant Mean Curvature Surfaces With Boundary

DOWNLOAD
Author : Rafael López
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-31

Constant Mean Curvature Surfaces With Boundary written by Rafael López 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 2013-08-31 with Mathematics categories.

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.

Surfaces With Constant Mean Curvature

DOWNLOAD
Author : Katsuei Kenmotsu
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Surfaces With Constant Mean Curvature written by Katsuei Kenmotsu 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 2003 with Mathematics categories.

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 objec

Constant Mean Curvature Surfaces In Homogeneous Manifolds

DOWNLOAD
Author : Julia Plehnert
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2012

Constant Mean Curvature Surfaces In Homogeneous Manifolds written by Julia Plehnert and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

In this dissertation new constant mean curvature surfaces in homogeneous 3-manifolds are constructed. They arise as sister surfaces of Plateau solutions. The first example, a two-parameter family of MC H surfaces in ∑(k) x R with H ∈ [0,1/2] and k + 4H2 ≤ 0, has genus 0,2 k ends and k-fold dihedral symmetry, k ≥ 2. The existence of the minimal sister follows from the construction of a mean convex domain. The projection of the domain is non-convex. The second example is an MC 1/2 surface in H2 ∈ R with k ends, genus 1 and k-fold dihedral symmetry, k ≥ 3. One has to solve two period problems in the construction. The first period guarantees that the surface has exactly one horizontal symmetry. For the second period the control of a horizontal mirror curve proves the dihedral symmetry. For H=1/2 all surfaces are Alexandrov-embedded.

Constant Mean Curvature Surfaces Harmonic Maps And Integrable Systems

DOWNLOAD
Author : Frederic Hélein
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Constant Mean Curvature Surfaces Harmonic Maps And Integrable Systems written by Frederic Hélein and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book intends to give an introduction to harmonic maps between a surface and a symmetric manifold and constant mean curvature surfaces as completely integrable systems. The presentation is accessible to undergraduate and graduate students in mathematics but will also be useful to researchers. It is among the first textbooks about integrable systems, their interplay with harmonic maps and the use of loop groups, and it presents the theory, for the first time, from the point of view of a differential geometer. The most important results are exposed with complete proofs (except for the last two chapters, which require a minimal knowledge from the reader). Some proofs have been completely rewritten with the objective, in particular, to clarify the relation between finite mean curvature tori, Wente tori and the loop group approach - an aspect largely neglected in the literature. The book helps the reader to access the ideas of the theory and to acquire a unified perspective of the subject.

Soap Bubble Clusters And Constant Mean Curvature Surfaces

DOWNLOAD
Author : Société mathématique de France. Journées
language : en
Publisher:
Release Date : 1993

Soap Bubble Clusters And Constant Mean Curvature Surfaces written by Société mathématique de France. Journées and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Calculus of variations categories.

Minimal Surfaces Integrable Systems And Visualisation

DOWNLOAD
Author : Tim Hoffmann
language : en
Publisher: Springer Nature
Release Date : 2021-05-06

Minimal Surfaces Integrable Systems And Visualisation written by Tim Hoffmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-06 with Mathematics categories.

This book collects original peer-reviewed contributions to the conferences organised by the international research network “Minimal surfaces: Integrable Systems and Visualization” financed by the Leverhulme Trust. The conferences took place in Cork, Granada, Munich and Leicester between 2016 and 2019. Within the theme of the network, the presented articles cover a broad range of topics and explore exciting links between problems related to the mean curvature of surfaces in homogeneous 3-manifolds, like minimal surfaces, CMC surfaces and mean curvature flows, integrable systems and visualisation. Combining research and overview articles by prominent international researchers, the book offers a valuable resource for both researchers and students who are interested in this research area.

New Developments In Differential Geometry Budapest 1996

DOWNLOAD
Author : J. Szenthe
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

New Developments In Differential Geometry Budapest 1996 written by J. Szenthe 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 2012-12-06 with Mathematics categories.

Proceedings of the Conference on Differential Geometry, Budapest, Hungary, July 27-30, 1996

The Motion Of A Surface By Its Mean Curvature

DOWNLOAD
Author : Kenneth A. Brakke
language : en
Publisher: Princeton University Press
Release Date : 2015-03-08

The Motion Of A Surface By Its Mean Curvature written by Kenneth A. Brakke 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 2015-03-08 with Mathematics categories.

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.

Lorentzian Geometry And Related Topics

DOWNLOAD
Author : María A. Cañadas-Pinedo
language : en
Publisher: Springer
Release Date : 2018-03-06

Lorentzian Geometry And Related Topics written by María A. Cañadas-Pinedo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-06 with Mathematics categories.

This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathematics and physics. This book is addressed to differential geometers, mathematical physicists and relativists, and graduate students interested in the field.

The Problem Of Plateau

DOWNLOAD
Author : Themistocles M. Rassias
language : en
Publisher: World Scientific
Release Date : 1992

The Problem Of Plateau written by Themistocles M. Rassias and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

This volume consists of papers written by eminent scientists from the international mathematical community, who present the latest information concerning the problem of Plateau after its classical solution by Jesse Douglas and Tibor Rad¢. The contributing papers provide insight and perspective on various problems in modern topics of Calculus of Variations, Global Differential Geometry and Global Nonlinear Analysis as related to the problem of Plateau.