Author: Richard M. Schoen
Publisher: International Press of Boston
ISBN:
Category : Mathematics
Languages : en
Pages : 414
Book Description
A presentation of research on harmonic maps, based on lectures given at the University of California, San Diego. Schoen has worked to use the Fells/Sampson theorem to reprove the rigidity theorem of Masfow and superrigidity theorem of Marqulis. Many of these developments are recorded here.
Lectures on Harmonic Maps
Author: Richard M. Schoen
Publisher: International Press of Boston
ISBN:
Category : Mathematics
Languages : en
Pages : 414
Book Description
A presentation of research on harmonic maps, based on lectures given at the University of California, San Diego. Schoen has worked to use the Fells/Sampson theorem to reprove the rigidity theorem of Masfow and superrigidity theorem of Marqulis. Many of these developments are recorded here.
Publisher: International Press of Boston
ISBN:
Category : Mathematics
Languages : en
Pages : 414
Book Description
A presentation of research on harmonic maps, based on lectures given at the University of California, San Diego. Schoen has worked to use the Fells/Sampson theorem to reprove the rigidity theorem of Masfow and superrigidity theorem of Marqulis. Many of these developments are recorded here.
Harmonic Mappings and Minimal Immersion
Author: Enrico Giusti
Publisher: Springer
ISBN: 3540397167
Category : Mathematics
Languages : en
Pages : 295
Book Description
Publisher: Springer
ISBN: 3540397167
Category : Mathematics
Languages : en
Pages : 295
Book Description
Harmonic Mappings and Minimal Immersion
Author: Centro internazionale matematico estivo
Publisher: C.I.M.E. Foundation Subseries
ISBN:
Category : Mathematics
Languages : en
Pages : 304
Book Description
Publisher: C.I.M.E. Foundation Subseries
ISBN:
Category : Mathematics
Languages : en
Pages : 304
Book Description
Lectures on harmonic maps
Theorems on Regularity and Singularity of Energy Minimizing Maps
Author: Leon Simon
Publisher: Birkhäuser
ISBN: 3034891938
Category : Mathematics
Languages : en
Pages : 160
Book Description
The aim of these lecture notes is to give an essentially self-contained introduction to the basic regularity theory for energy minimizing maps, including recent developments concerning the structure of the singular set and asymptotics on approach to the singular set. Specialized knowledge in partial differential equations or the geometric calculus of variations is not required; a good general background in mathematical analysis would be adequate preparation.
Publisher: Birkhäuser
ISBN: 3034891938
Category : Mathematics
Languages : en
Pages : 160
Book Description
The aim of these lecture notes is to give an essentially self-contained introduction to the basic regularity theory for energy minimizing maps, including recent developments concerning the structure of the singular set and asymptotics on approach to the singular set. Specialized knowledge in partial differential equations or the geometric calculus of variations is not required; a good general background in mathematical analysis would be adequate preparation.
Lectures on Harmonic Maps
Harmonic Mappings and Minimal Immersions
Author: Centro internazionale matematico estivo
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 312
Book Description
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 312
Book Description
Lectures on Harmonic Analysis
Author: Thomas H. Wolff
Publisher: American Mathematical Soc.
ISBN: 0821834495
Category : Mathematics
Languages : en
Pages : 154
Book Description
This book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is both an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The usual background material is covered in the first few chapters: the Fourier transform, convolution, the inversion theorem, the uncertainty principle and the method of stationary phase. However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in the later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for further reading and research. Technicalities are kept to a minimum, and simpler but more basic methods are often favored over the most recent methods. The clear style of the exposition and the quick progression from fundamentals to advanced topics ensures that both graduate students and research mathematicians will benefit from the book.
Publisher: American Mathematical Soc.
ISBN: 0821834495
Category : Mathematics
Languages : en
Pages : 154
Book Description
This book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is both an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The usual background material is covered in the first few chapters: the Fourier transform, convolution, the inversion theorem, the uncertainty principle and the method of stationary phase. However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in the later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for further reading and research. Technicalities are kept to a minimum, and simpler but more basic methods are often favored over the most recent methods. The clear style of the exposition and the quick progression from fundamentals to advanced topics ensures that both graduate students and research mathematicians will benefit from the book.
Selected Topics in Harmonic Maps
Author: James Eells
Publisher: American Mathematical Soc.
ISBN: 0821807005
Category : Mathematics
Languages : en
Pages : 93
Book Description
Gives an account of the various aspects of the theory of harmonic maps between Riemannian manifolds. This book presents an exposition of the qualitative aspects of harmonic maps. It also proposes certain unsolved problems, together with comments and references, which are of widely varying difficulty.
Publisher: American Mathematical Soc.
ISBN: 0821807005
Category : Mathematics
Languages : en
Pages : 93
Book Description
Gives an account of the various aspects of the theory of harmonic maps between Riemannian manifolds. This book presents an exposition of the qualitative aspects of harmonic maps. It also proposes certain unsolved problems, together with comments and references, which are of widely varying difficulty.
The Analysis Of Harmonic Maps And Their Heat Flows
Author: Fanghua Lin
Publisher: World Scientific
ISBN: 9814472247
Category : Mathematics
Languages : en
Pages : 280
Book Description
This book provides a broad yet comprehensive introduction to the analysis of harmonic maps and their heat flows. The first part of the book contains many important theorems on the regularity of minimizing harmonic maps by Schoen-Uhlenbeck, stationary harmonic maps between Riemannian manifolds in higher dimensions by Evans and Bethuel, and weakly harmonic maps from Riemannian surfaces by Helein, as well as on the structure of a singular set of minimizing harmonic maps and stationary harmonic maps by Simon and Lin. The second part of the book contains a systematic coverage of heat flow of harmonic maps that includes Eells-Sampson's theorem on global smooth solutions, Struwe's almost regular solutions in dimension two, Sacks-Uhlenbeck's blow-up analysis in dimension two, Chen-Struwe's existence theorem on partially smooth solutions, and blow-up analysis in higher dimensions by Lin and Wang.The book can be used as a textbook for the topic course of advanced graduate students and for researchers who are interested in geometric partial differential equations and geometric analysis.
Publisher: World Scientific
ISBN: 9814472247
Category : Mathematics
Languages : en
Pages : 280
Book Description
This book provides a broad yet comprehensive introduction to the analysis of harmonic maps and their heat flows. The first part of the book contains many important theorems on the regularity of minimizing harmonic maps by Schoen-Uhlenbeck, stationary harmonic maps between Riemannian manifolds in higher dimensions by Evans and Bethuel, and weakly harmonic maps from Riemannian surfaces by Helein, as well as on the structure of a singular set of minimizing harmonic maps and stationary harmonic maps by Simon and Lin. The second part of the book contains a systematic coverage of heat flow of harmonic maps that includes Eells-Sampson's theorem on global smooth solutions, Struwe's almost regular solutions in dimension two, Sacks-Uhlenbeck's blow-up analysis in dimension two, Chen-Struwe's existence theorem on partially smooth solutions, and blow-up analysis in higher dimensions by Lin and Wang.The book can be used as a textbook for the topic course of advanced graduate students and for researchers who are interested in geometric partial differential equations and geometric analysis.