Tsing Hua Lectures on Geometry & Analysis PDF Download
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Author: Shing-Tung Yau
Publisher: International Press of Boston
ISBN:
Category : Mathematics
Languages : en
Pages : 336
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Book Description
A collection of lectures given by the author and numerous contributors at Tsing Hua University, Taiwan, in 1990-1. Topics covered include: energy in general relativity; existence and convergence of solutions; closed geodesics; and mean curvature evolution.
Author: Shing-Tung Yau
Publisher: International Press of Boston
ISBN:
Category : Mathematics
Languages : en
Pages : 336
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Book Description
A collection of lectures given by the author and numerous contributors at Tsing Hua University, Taiwan, in 1990-1. Topics covered include: energy in general relativity; existence and convergence of solutions; closed geodesics; and mean curvature evolution.
Author: Audrey Terras
Publisher: Cambridge University Press
ISBN: 9780521457187
Category : Mathematics
Languages : en
Pages : 456
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Book Description
It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.
Author: Dorian Goldfeld
Publisher: Springer Science & Business Media
ISBN: 1461412595
Category : Mathematics
Languages : en
Pages : 715
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Book Description
In honor of Serge Lang’s vast contribution to mathematics, this memorial volume presents articles by prominent mathematicians. Reflecting the breadth of Lang's own interests and accomplishments, these essays span the field of Number Theory, Analysis and Geometry.
Author: Jürgen Jost
Publisher: Springer Science & Business Media
ISBN: 3642005411
Category : Mathematics
Languages : en
Pages : 226
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Book Description
"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.
Author: Bennett Chow
Publisher: American Mathematical Soc.
ISBN: 0821846612
Category : Mathematics
Languages : en
Pages : 542
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Book Description
The Ricci flow uses methods from analysis to study the geometry and topology of manifolds. With the third part of their volume on techniques and applications of the theory, the authors give a presentation of Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject, with an emphasis on the geometric and analytic aspects. The topics include Perelman's entropy functional, point picking methods, aspects of Perelman's theory of $\kappa$-solutions including the $\kappa$-gap theorem, compactness theorem and derivative estimates, Perelman's pseudolocality theorem, and aspects of the heat equation with respect to static and evolving metrics related to Ricci flow. In the appendices, we review metric and Riemannian geometry including the space of points at infinity and Sharafutdinov retraction for complete noncompact manifolds with nonnegative sectional curvature. As in the previous volumes, the authors have endeavored, as much as possible, to make the chapters independent of each other. The book makes advanced material accessible to graduate students and nonexperts. It includes a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors give the appropriate references so that the reader may further pursue the statements and proofs of the various results.
Author: Carlo Mantegazza
Publisher: Springer Science & Business Media
ISBN: 3034801459
Category : Mathematics
Languages : en
Pages : 175
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Book Description
This book is an introduction to the subject of mean curvature flow of hypersurfaces with special emphasis on the analysis of singularities. This flow occurs in the description of the evolution of numerous physical models where the energy is given by the area of the interfaces. These notes provide a detailed discussion of the classical parametric approach (mainly developed by R. Hamilton and G. Huisken). They are well suited for a course at PhD/PostDoc level and can be useful for any researcher interested in a solid introduction to the technical issues of the field. All the proofs are carefully written, often simplified, and contain several comments. Moreover, the author revisited and organized a large amount of material scattered around in literature in the last 25 years.
Author: Fanghua Lin
Publisher: World Scientific
ISBN: 9814472247
Category : Mathematics
Languages : en
Pages : 280
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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.
Author: C. S. Aravinda
Publisher: Cambridge University Press
ISBN: 1316539180
Category : Mathematics
Languages : en
Pages : 378
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Book Description
The ICM 2010 satellite conference 'Geometry, Topology and Dynamics in Negative Curvature' afforded an excellent opportunity to discuss various aspects of this fascinating interdisciplinary subject in which methods and techniques from geometry, topology, and dynamics often interact in novel and interesting ways. Containing ten survey articles written by some of the leading experts in the field, this proceedings volume provides an overview of important recent developments relating to negative curvature. Topics covered include homogeneous dynamics, harmonic manifolds, the Atiyah Conjecture, counting circles and arcs, and hyperbolic buildings. Each author pays particular attention to the expository aspects, making the book particularly useful for graduate students and mathematicians interested in transitioning from other areas via the common theme of negative curvature.
Author: Akito Futaki
Publisher: Springer
ISBN: 4431560211
Category : Mathematics
Languages : en
Pages : 350
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Book Description
Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincaré conjecture, the Yau–Tian–Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the Strominger–Yau–Zaslow conjecture on mirror symmetry, the relative Yau–Tian–Donaldson conjecture in Kähler geometry, the Hopf conjecture, and the Yau conjecture on the first eigenvalue of an embedded minimal hypersurface of the sphere. For the younger generation to approach such problems and obtain the required techniques, it is of the utmost importance to provide them with up-to-date information from leading specialists.The geometry conference for the friendship of China and Japan has achieved this purpose during the past 10 years. Their talks deal with problems at the highest level, often accompanied with solutions and ideas, which extend across various fields in Riemannian geometry, symplectic and contact geometry, and complex geometry.
Author: E. Brian Davies
Publisher: Cambridge University Press
ISBN: 0521777496
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Authoritative lectures from world experts on spectral theory and geometry.
