Geometry of Harmonic Maps:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser Boston
1996
|
| Series: | Progress in Nonlinear Differential Equations and Their Applications
23 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Harmonic maps are solutions to a natural geometrical variational problem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics, and to the theory of liquid crystals in materials science. During the past thirty years this subject has been developed extensively. The monograph is by no means intended to give a complete description of the theory of harmonic maps. For example, the book excludes a large part of the theory of harmonic maps from 2-dimensional domains, where the methods are quite different from those discussed here. The first chapter consists of introductory material. Several equivalent definitions of harmonic maps are described, and interesting examples are presented. Various important properties and formulas are derived. Among them are Bochner-type formula for the energy density and the second variational formula. This chapter serves not only as a basis for the later chapters, but also as a brief introduction to the theory. Chapter 2 is devoted to the conservation law of harmonic maps. Emphasis is placed on applications of conservation law to the mono tonicity formula and Liouville-type theorems |
| Physical Description: | 1 Online-Ressource (X, 246 p) |
| ISBN: | 9781461240846 9781461286448 |
| DOI: | 10.1007/978-1-4612-4084-6 |
Staff View
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| 490 | 1 | |a Progress in Nonlinear Differential Equations and Their Applications |v 23 | |
| 500 | |a Harmonic maps are solutions to a natural geometrical variational problem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics, and to the theory of liquid crystals in materials science. During the past thirty years this subject has been developed extensively. The monograph is by no means intended to give a complete description of the theory of harmonic maps. For example, the book excludes a large part of the theory of harmonic maps from 2-dimensional domains, where the methods are quite different from those discussed here. The first chapter consists of introductory material. Several equivalent definitions of harmonic maps are described, and interesting examples are presented. Various important properties and formulas are derived. Among them are Bochner-type formula for the energy density and the second variational formula. This chapter serves not only as a basis for the later chapters, but also as a brief introduction to the theory. Chapter 2 is devoted to the conservation law of harmonic maps. Emphasis is placed on applications of conservation law to the mono tonicity formula and Liouville-type theorems | ||
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Record in the Search Index
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| any_adam_object | |
| author | Xin, Yuanlong |
| author_facet | Xin, Yuanlong |
| author_role | aut |
| author_sort | Xin, Yuanlong |
| author_variant | y x yx |
| building | Verbundindex |
| bvnumber | BV042420211 |
| classification_tum | MAT 000 |
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| ctrlnum | (OCoLC)1165460911 (DE-599)BVBBV042420211 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-4084-6 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461240846 9781461286448 |
| language | English |
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| series | Progress in Nonlinear Differential Equations and Their Applications |
| series2 | Progress in Nonlinear Differential Equations and Their Applications |
| spelling | Xin, Yuanlong Verfasser aut Geometry of Harmonic Maps by Yuanlong Xin Boston, MA Birkhäuser Boston 1996 1 Online-Ressource (X, 246 p) txt rdacontent c rdamedia cr rdacarrier Progress in Nonlinear Differential Equations and Their Applications 23 Harmonic maps are solutions to a natural geometrical variational problem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics, and to the theory of liquid crystals in materials science. During the past thirty years this subject has been developed extensively. The monograph is by no means intended to give a complete description of the theory of harmonic maps. For example, the book excludes a large part of the theory of harmonic maps from 2-dimensional domains, where the methods are quite different from those discussed here. The first chapter consists of introductory material. Several equivalent definitions of harmonic maps are described, and interesting examples are presented. Various important properties and formulas are derived. Among them are Bochner-type formula for the energy density and the second variational formula. This chapter serves not only as a basis for the later chapters, but also as a brief introduction to the theory. Chapter 2 is devoted to the conservation law of harmonic maps. Emphasis is placed on applications of conservation law to the mono tonicity formula and Liouville-type theorems Mathematics Differential equations, partial Global differential geometry Distribution (Probability theory) Mathematical physics Materials Differential Geometry Partial Differential Equations Several Complex Variables and Analytic Spaces Probability Theory and Stochastic Processes Mathematical Methods in Physics Continuum Mechanics and Mechanics of Materials Mathematik Mathematische Physik Harmonische Abbildung (DE-588)4023452-6 gnd rswk-swf Harmonische Abbildung (DE-588)4023452-6 s 1\p DE-604 Progress in Nonlinear Differential Equations and Their Applications 23 (DE-604)BV036582883 23 https://doi.org/10.1007/978-1-4612-4084-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Xin, Yuanlong Geometry of Harmonic Maps Progress in Nonlinear Differential Equations and Their Applications Mathematics Differential equations, partial Global differential geometry Distribution (Probability theory) Mathematical physics Materials Differential Geometry Partial Differential Equations Several Complex Variables and Analytic Spaces Probability Theory and Stochastic Processes Mathematical Methods in Physics Continuum Mechanics and Mechanics of Materials Mathematik Mathematische Physik Harmonische Abbildung (DE-588)4023452-6 gnd |
| subject_GND | (DE-588)4023452-6 |
| title | Geometry of Harmonic Maps |
| title_auth | Geometry of Harmonic Maps |
| title_exact_search | Geometry of Harmonic Maps |
| title_full | Geometry of Harmonic Maps by Yuanlong Xin |
| title_fullStr | Geometry of Harmonic Maps by Yuanlong Xin |
| title_full_unstemmed | Geometry of Harmonic Maps by Yuanlong Xin |
| title_short | Geometry of Harmonic Maps |
| title_sort | geometry of harmonic maps |
| topic | Mathematics Differential equations, partial Global differential geometry Distribution (Probability theory) Mathematical physics Materials Differential Geometry Partial Differential Equations Several Complex Variables and Analytic Spaces Probability Theory and Stochastic Processes Mathematical Methods in Physics Continuum Mechanics and Mechanics of Materials Mathematik Mathematische Physik Harmonische Abbildung (DE-588)4023452-6 gnd |
| topic_facet | Mathematics Differential equations, partial Global differential geometry Distribution (Probability theory) Mathematical physics Materials Differential Geometry Partial Differential Equations Several Complex Variables and Analytic Spaces Probability Theory and Stochastic Processes Mathematical Methods in Physics Continuum Mechanics and Mechanics of Materials Mathematik Mathematische Physik Harmonische Abbildung |
| url | https://doi.org/10.1007/978-1-4612-4084-6 |
| volume_link | (DE-604)BV036582883 |
| work_keys_str_mv | AT xinyuanlong geometryofharmonicmaps |