Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. In includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.” (Peter Lax, SIAM review, June 1998).

Differential equations. --- Manifolds (Mathematics). --- Differential Equations. --- Manifolds and Cell Complexes. --- Equacions diferencials funcionals --- Varietats (Matemàtica) --- Manifolds (Mathematics)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Contact manifolds. --- Submanifolds. --- Geometry. --- Geometry, Differential --- Manifolds (Mathematics) --- Manifolds, Contact --- Almost contact manifolds --- Differentiable manifolds --- Mathematics --- Euclid's Elements --- Subvarietats (Matemàtica) --- Geometria diferencial --- Varietats (Matemàtica)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In the middle of the last century, after hearing a talk of Mostow on one of his rigidity theorems, Borel conjectured in a letter to Serre a purely topological version of rigidity for aspherical manifolds (i.e. manifolds with contractible universal covers). The Borel conjecture is now one of the central problems of topology with many implications for manifolds that need not be aspherical. Since then, the theory of rigidity has vastly expanded in both precision and scope. This book rethinks the implications of accepting his heuristic as a source of ideas. Doing so leads to many variants of the original conjecture - some true, some false, and some that remain conjectural. The author explores this collection of ideas, following them where they lead whether into rigidity theory in its differential geometric and representation theoretic forms, or geometric group theory, metric geometry, global analysis, algebraic geometry, K-theory, or controlled topology.

Rigidity (Geometry) --- Manifolds (Mathematics) --- Three-manifolds (Topology) --- Graph theory. --- Rigidesa (Geometria) --- Varietats (Matemàtica) --- Varietats topològiques de dimensió 3 --- Teoria de grafs

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book provides an up-to-date introduction to the theory of manifolds, submanifolds, semi-Riemannian geometry and warped product geometry, and their applications in geometry and physics. It then explores the properties of conformal vector fields and conformal transformations, including their fixed points, essentiality and the Lichnerowicz conjecture. Later chapters focus on the study of conformal vector fields on special Riemannian and Lorentzian manifolds, with a special emphasis on general relativistic spacetimes and the evolution of conformal vector fields in terms of initial data. The book also delves into the realm of Ricci flow and Ricci solitons, starting with motivations and basic results and moving on to more advanced topics within the framework of Riemannian geometry. The main emphasis of the book is on the interplay between conformal vector fields and Ricci solitons, and their applications in contact geometry. The book highlights the fact that Nil-solitons and Sol-solitons naturally arise in the study of Ricci solitons in contact geometry. Finally, the book gives a comprehensive overview of generalized quasi-Einstein structures and Yamabe solitons and their roles in contact geometry. It would serve as a valuable resource for graduate students and researchers in mathematics and physics as well as those interested in the intersection of geometry and physics.

Global analysis (Mathematics). --- Manifolds (Mathematics). --- Geometry, Differential. --- General relativity (Physics). --- Global Analysis and Analysis on Manifolds. --- Differential Geometry. --- General Relativity. --- Conformal geometry. --- Ricci flow. --- Geometria conforme --- Varietats (Matemàtica) --- Global analysis (Mathematics) --- Manifolds (Mathematics) --- General relativity (Physics)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Geometry, Differential. --- Differential geometry --- Geometria diferencial --- Geometria --- Càlcul de tensors --- Connexions (Matemàtica) --- Coordenades --- Corbes --- Cossos convexos --- Dominis convexos --- Espais de curvatura constant --- Espais simètrics --- Estructures hermitianes --- Formes diferencials --- G-estructures --- Geodèsiques (Matemàtica) --- Geometria de Riemann --- Geometria diferencial global --- Geometria integral --- Geometria simplèctica --- Hiperespai --- Subvarietats (Matemàtica) --- Topologia diferencial --- Varietats (Matemàtica) --- Varietats de Kähler