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Harmonic Maps and Minimal Immersions with Symmetries

1993 Mathematics
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Release : 1993
Genre : Mathematics
Kind : eBook
Book Rating : 498/5 ( reviews)

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Book Synopsis Harmonic Maps and Minimal Immersions with Symmetries by : James Eells

Download or read book Harmonic Maps and Minimal Immersions with Symmetries written by James Eells. This book was released on 1993. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.

Harmonic Maps and Minimal Immersions with Symmetries (AM-130), Volume 130

2016-03-02 Mathematics
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Release : 2016-03-02
Genre : Mathematics
Kind : eBook
Book Rating : 508/5 ( reviews)

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Book Synopsis Harmonic Maps and Minimal Immersions with Symmetries (AM-130), Volume 130 by : James Eells

Download or read book Harmonic Maps and Minimal Immersions with Symmetries (AM-130), Volume 130 written by James Eells. This book was released on 2016-03-02. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.

Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 614/5 ( reviews)

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Book Synopsis Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli by : Gabor Toth

Download or read book Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli written by Gabor Toth. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: "Spherical soap bubbles", isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between algebra and geometry. In this accessible book, the author traces the development of the study of spherical minimal immersions over the past 30 plus years, including a valuable selection of exercises.

Harmonic Morphisms, Harmonic Maps and Related Topics

1999-10-13 Mathematics
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Release : 1999-10-13
Genre : Mathematics
Kind : eBook
Book Rating : 325/5 ( reviews)

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Book Synopsis Harmonic Morphisms, Harmonic Maps and Related Topics by : Christopher Kum Anand

Download or read book Harmonic Morphisms, Harmonic Maps and Related Topics written by Christopher Kum Anand. This book was released on 1999-10-13. Available in PDF, EPUB and Kindle. Book excerpt: The subject of harmonic morphisms is relatively new but has attracted a huge worldwide following. Mathematicians, young researchers and distinguished experts came from all corners of the globe to the City of Brest - site of the first, international conference devoted to the fledgling but dynamic field of harmonic morphisms. Harmonic Morphisms, Harmonic Maps, and Related Topics reports the proceedings of that conference, forms the first work primarily devoted to harmonic morphisms, bringing together contributions from the founders of the subject, leading specialists, and experts in other related fields. Starting with "The Beginnings of Harmonic Morphisms," which provides the essential background, the first section includes papers on the stability of harmonic morphisms, global properties, harmonic polynomial morphisms, Bochner technique, f-structures, symplectic harmonic morphisms, and discrete harmonic morphisms. The second section addresses the wider domain of harmonic maps and contains some of the most recent results on harmonic maps and surfaces. The final section highlights the rapidly developing subject of constant mean curvature surfaces. Harmonic Morphisms, Harmonic Maps, and Related Topics offers a coherent, balanced account of this fast-growing subject that furnishes a vital reference for anyone working in the field.

Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields

2013-06-18 Mathematics
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Release : 2013-06-18
Genre : Mathematics
Kind : eBook
Book Rating : 349/5 ( reviews)

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Book Synopsis Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields by : Yuan-Jen Chiang

Download or read book Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields written by Yuan-Jen Chiang. This book was released on 2013-06-18. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced by Guoying Jiang in 1986. The book presents an overview of the important developments made in these fields since they first came up. Furthermore, it introduces biwave maps (generalizing wave maps) which were first studied by the author in 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated by Toshiyuki Ichiyama, Jun-Ichi Inoguchi and Hajime Urakawa in 2008. Other topics discussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields.

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