Constant Mean Curvature Surfaces In Homogeneous Manifolds

Author : Julia Plehnert
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832532064
Total Pages : 94 pages
Book Rating : 4.62/5 ( download)

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Download or read book Constant Mean Curvature Surfaces in Homogeneous Manifolds written by Julia Plehnert and published by Logos Verlag Berlin GmbH. This book was released on 2012 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Rafael López
Publisher : Springer Science & Business Media
ISBN 13 : 3642396267
Total Pages : 296 pages
Book Rating : 4.67/5 ( download)

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Download or read book Constant Mean Curvature Surfaces with Boundary written by Rafael López and published by Springer Science & Business Media. This book was released on 2013-08-31 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Frederic Hélein
Publisher : Springer Science & Business Media
ISBN 13 : 9783764365769
Total Pages : 132 pages
Book Rating : 4.65/5 ( download)

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Download or read book Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems written by Frederic Hélein and published by Springer Science & Business Media. This book was released on 2001-06-01 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book helps the reader to access the ideas of the theory and to acquire a united perspective of the subject."--BOOK JACKET.

Author : Antonio Alarcón
Publisher : Springer Nature
ISBN 13 : 3031399161
Total Pages : 398 pages
Book Rating : 4.69/5 ( download)

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Download or read book New Trends in Geometric Analysis written by Antonio Alarcón and published by Springer Nature. This book was released on 2023-11-25 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide an overview of some of the progress made by the Spanish Network of Geometric Analysis (REAG, by its Spanish acronym) since its born in 2007. REAG was created with the objective of enabling the interchange of ideas and the knowledge transfer between several Spanish groups having Geometric Analysis as a common research line. This includes nine groups at Universidad Autónoma de Barcelona, Universidad Autónoma de Madrid, Universidad de Granada, Universidad Jaume I de Castellón, Universidad de Murcia, Universidad de Santiago de Compostela and Universidad de Valencia. The success of REAG has been substantiated with regular meetings and the publication of research papers obtained in collaboration between the members of different nodes. On the occasion of the 15th anniversary of REAG this book aims to collect some old and new contributions of this network to Geometric Analysis. The book consists of thirteen independent chapters, all of them authored by current members of REAG. The topics under study cover geometric flows, constant mean curvature surfaces in Riemannian and sub-Riemannian spaces, integral geometry, potential theory and Riemannian geometry, among others. Some of these chapters have been written in collaboration between members of different nodes of the network, and show the fruitfulness of the common research atmosphere provided by REAG. The rest of the chapters survey a research line or present recent progresses within a group of those forming REAG. Surveying several research lines and offering new directions in the field, the volume is addressed to researchers (including postdocs and PhD students) in Geometric Analysis in the large.

Author : Joaqu’n PŽrez
Publisher : American Mathematical Soc.
ISBN 13 : 0821849921
Total Pages : 198 pages
Book Rating : 4.27/5 ( download)

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Download or read book Geometric Analysis written by Joaqu’n PŽrez and published by American Mathematical Soc.. This book was released on 2012-07-16 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains research and expository articles from the courses and talks given at the RSME Lluis A. Santalo Summer School, ``Geometric Analysis'', held June 28-July 2, 2010, in Granada, Spain. The goal of the Summer School was to present some of the many advances currently taking place in the interaction between partial differential equations and differential geometry, with special emphasis on the theory of minimal surfaces. This volume includes expository articles about the current state of specific problems involving curvature and partial differential equations, with interactions to neighboring fields such as probability. An introductory, mostly self-contained course on constant mean curvature surfaces in Lie groups equipped with a left invariant metric is provided. The volume will be of interest to researchers, post-docs, and advanced PhD students in the interface between partial differential equations and differential geometry.

Author : Katsuei Kenmotsu
Publisher : American Mathematical Soc.
ISBN 13 : 9780821834794
Total Pages : 142 pages
Book Rating : 4.97/5 ( download)

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Download or read book Surfaces with Constant Mean Curvature written by Katsuei Kenmotsu and published by American Mathematical Soc.. This book was released on 2003 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. 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. A trivial 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. In this book, the author presents the numerous examples of constant mean curvature surfaces and the techniques for studying them. Many figures illustrate the presented results and allow the reader to visualize and better understand these beautiful objects.

Author : Bennett Palmer
Publisher :
ISBN 13 :
Total Pages : 156 pages
Book Rating : 4.03/5 ( download)

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Download or read book Surfaces of Constant Mean Curvature in Space Forms written by Bennett Palmer and published by . This book was released on 1986 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : David A. Hoffman
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.98/5 ( download)

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Download or read book Surfaces in Constant Curvature Manifolds with Parallel Mean Curvature Vector Field written by David A. Hoffman and published by . This book was released on 1971 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Bang-Yen Chen
Publisher : World Scientific Publishing Company
ISBN 13 : 9814616710
Total Pages : 488 pages
Book Rating : 4.13/5 ( download)

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Download or read book Total Mean Curvature and Submanifolds of Finite Type written by Bang-Yen Chen and published by World Scientific Publishing Company. This book was released on 2014-10-29 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last four decades, there were numerous important developments on total mean curvature and the theory of finite type submanifolds. This unique and expanded second edition comprises a comprehensive account of the latest updates and new results that cover total mean curvature and submanifolds of finite type. The longstanding biharmonic conjecture of the author's and the generalized biharmonic conjectures are also presented in details. This book will be of use to graduate students and researchers in the field of geometry.

Author : Luc Vrancken
Publisher : Lulu.com
ISBN 13 : 1847990169
Total Pages : 266 pages
Book Rating : 4.67/5 ( download)

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Download or read book Symposium on the Differential Geometry of Submanifolds written by Luc Vrancken and published by Lulu.com. This book was released on 2008-06-30 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the «Symposium on differential geometry» which took place at the Université de Valenciennes et du Hainaut Cambrésis from July 3, 2007 until July 7, 2007.The main theme of the conference was the differential geometry of submanifolds. Special emphasis was put on the following topics:Lagrangian immersions, Minimal immersions and constant mean curvature immersions, Harmonic maps and harmonic morphisms, Variational problems, Affine differential geometry. This conference follows the tradition of the conferences in the series of « Geometry and Topology of Submanifolds », which started with the Luminy meeting in 1987 and then continued with various meetings at different places in Europe, such as amongst others Avignon, Leeds, Leuven, Brussels, Nordfjordeid, Berlin, Warszawa, Bedlewo and also in China (Beijing, 1998).