1# Library to Find Best eBook for Read
Author : Peter Li
Release : 2012-05-03
Genre : Mathematics
Kind : eBook
Book Rating : 646/5 ( reviews)
Book Synopsis Geometric Analysis by : Peter Li
Download or read book Geometric Analysis written by Peter Li. This book was released on 2012-05-03. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text demonstrates the basic techniques for researchers interested in the field of geometric analysis.
Author : Iva Stavrov
Release : 2020-11-12
Genre : Education
Kind : eBook
Book Rating : 281/5 ( reviews)
Book Synopsis Curvature of Space and Time, with an Introduction to Geometric Analysis by : Iva Stavrov
Download or read book Curvature of Space and Time, with an Introduction to Geometric Analysis written by Iva Stavrov. This book was released on 2020-11-12. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations. After addressing concepts in geometry such as metrics, covariant differentiation, tensor calculus and curvature, the book explains the mathematical framework for both special and general relativity. Relativistic concepts discussed include (initial value formulation of) the Einstein equations, stress-energy tensor, Schwarzschild space-time, ADM mass and geodesic incompleteness. The concluding chapters of the book introduce the reader to geometric analysis: original results of the author and her undergraduate student collaborators illustrate how methods of analysis and differential equations are used in addressing questions from geometry and relativity. The book is mostly self-contained and the reader is only expected to have a solid foundation in multivariable and vector calculus and linear algebra. The material in this book was first developed for the 2013 summer program in geometric analysis at the Park City Math Institute, and was recently modified and expanded to reflect the author's experience of teaching mathematical general relativity to advanced undergraduates at Lewis & Clark College.
Author : Alexander Brudnyi
Release : 2011-10-07
Genre : Mathematics
Kind : eBook
Book Rating : 099/5 ( reviews)
Book Synopsis Methods of Geometric Analysis in Extension and Trace Problems by : Alexander Brudnyi
Download or read book Methods of Geometric Analysis in Extension and Trace Problems written by Alexander Brudnyi. This book was released on 2011-10-07. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by the aforementioned problems the book also is unified by geometric analysis approach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric space theory to Riemannian and coarse geometry and more. The necessary facts are presented mostly with detailed proofs to make the book accessible to a wide audience.
Author : Steven George Krantz
Release : 1993-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 251/5 ( reviews)
Book Synopsis Geometric Analysis and Function Spaces by : Steven George Krantz
Download or read book Geometric Analysis and Function Spaces written by Steven George Krantz. This book was released on 1993-01-01. Available in PDF, EPUB and Kindle. Book excerpt: This book brings into focus the synergistic interaction between analysis and geometry by examining a variety of topics in function theory, real analysis, harmonic analysis, several complex variables, and group actions. Krantz's approach is motivated by examples, both classical and modern, which highlight the symbiotic relationship between analysis and geometry. Creating a synthesis among a host of different topics, this book is useful to researchers in geometry and analysis and may be of interest to physicists, astronomers, and engineers in certain areas. The book is based on lectures presented at an NSF-CBMS Regional Conference held in May 1992.
Author : Stefano Pigola
Release : 2008-05-28
Genre : Mathematics
Kind : eBook
Book Rating : 428/5 ( reviews)
Book Synopsis Vanishing and Finiteness Results in Geometric Analysis by : Stefano Pigola
Download or read book Vanishing and Finiteness Results in Geometric Analysis written by Stefano Pigola. This book was released on 2008-05-28. Available in PDF, EPUB and Kindle. Book excerpt: This book describes very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods, from spectral theory and qualitative properties of solutions of PDEs, to comparison theorems in Riemannian geometry and potential theory.
