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  3. Analysis on Manifolds

The Art of Gluing Space-Time Manifolds: Methods and Applications

Posted By: AvaxGenius
Date: 20 Dec 2023 04:33:16
The Art of Gluing Space-Time Manifolds: Methods and Applications

The Art of Gluing Space-Time Manifolds: Methods and Applications by Samad Khakshournia , Reza Mansouri
English | PDF EPUB (True) | 2023 | 126 Pages | ISBN : 3031486110 | 9.7 MB

This concise book reviews methods used for gluing space-time manifolds together. It is therefore relevant to theorists working on branes, walls, domain walls, concepts frequently used in theoretical cosmology, astrophysics, and gravity theory. Nowadays, applications are also in theoretical condensed matter physics where Riemannian geometry appears. The book also reviews the history of matching conditions between two space-time manifolds from the early times of general relativity up to now.
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Vector Analysis Versus Vector Calculus

Posted By: AvaxGenius
Date: 10 Jun 2023 11:57:51
Vector Analysis Versus Vector Calculus

Vector Analysis Versus Vector Calculus by Antonio Galbis , Manuel Maestre
English | PDF(True) | 2012 | 383 Pages | ISBN : 1461421993 | 4 MB

The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text takes a differential geometric point of view and provides for the student a bridge between pure and applied mathematics by carefully building a formal rigorous development of the topic and following this through to concrete applications in two and three variables. Several practical methods and many solved exercises are provided. This book tries to show that vector analysis and vector calculus are not always at odds with one another.
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Some Nonlinear Problems in Riemannian Geometry

Posted By: AvaxGenius
Date: 22 Mar 2023 18:20:46
Some Nonlinear Problems in Riemannian Geometry

Some Nonlinear Problems in Riemannian Geometry by Thierry Aubin
English | PDF (True) | 1998 | 414 Pages | ISBN : 3540607528 | 33.23 MB

During the last few years, the field of nonlinear problems has undergone great development. This book consisting of the updated Grundlehren volume 252 by the author and of a newly written part, deals with some important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved. Each problem is explained, up-to-date results are given and proofs are presented. Thus, the reader is given access, for each specific problem, to its present status of solution as well as to the most up-to-date methods for approaching it. The main objective of the book is to explain some methods and new techniques, and to apply them. It deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber.
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Integrable Systems in the Realm of Algebraic Geometry (Repost)

Posted By: AvaxGenius
Date: 27 Jan 2023 17:04:43
Integrable Systems in the Realm of Algebraic Geometry (Repost)

Integrable Systems in the Realm of Algebraic Geometry by Pol Vanhaecke
English | PDF | 2001 | 78 Pages | ISBN : 3540423370 | 95.3 MB

This book treats the general theory of Poisson structures and integrable systems on affine varieties in a systematic way. Special attention is drawn to algebraic completely integrable systems. Several integrable systems are constructed and studied in detail and a few applications of integrable systems to algebraic geometry are worked out. In the second edition some of the concepts in Poisson geometry are clarified by introducting Poisson cohomology; the Mumford systems are constructed from the algebra of pseudo-differential operators, which clarifies their origin; a new explanation of the multi Hamiltonian structure of the Mumford systems is given by using the loop algebra of sl(2); and finally Goedesic flow on SO(4) is added to illustrate the linearizatin algorith and to give another application of integrable systems to algebraic geometry.
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Operator Theory

Posted By: AvaxGenius
Date: 20 Aug 2022 05:25:45
Operator Theory

Operator Theory by Daniel Alpay
English | PDF(True) | 2015 | 1847 Pages | ISBN : 3034806663 | 17.9 MB

A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.
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Mean Curvature Flow and Isoperimetric Inequalities

Posted By: AvaxGenius
Date: 16 Apr 2022 21:30:42
Mean Curvature Flow and Isoperimetric Inequalities

Mean Curvature Flow and Isoperimetric Inequalities by Manuel Ritoré
English | PDF | 2010 | 113 Pages | ISBN : 303460212X | 0.98 MB

Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized.
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