Download or read book Complex Monge Amp re Equations and Geodesics in the Space of K hler Metrics written by Vincent Guedj and published by Springer. This book was released on 2012-01-05 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of these lecture notes is to provide an introduction to the theory of complex Monge–Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (Kähler–Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford–Taylor), Monge–Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi–Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli–Kohn–Nirenberg–Spruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after Phong–Sturm and Berndtsson). Each chapter can be read independently and is based on a series of lectures by R. Berman, Z. Blocki, S. Boucksom, F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, delivered to non-experts. The book is thus addressed to any mathematician with some interest in one of the following fields, complex differential geometry, complex analysis, complex dynamics, fully non-linear PDE's and stochastic analysis.

Download or read book Spectral Geometry written by Pierre H. Berard and published by Springer. This book was released on 2006-11-14 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Matrix Information Geometry written by Frank Nielsen and published by Springer Science & Business Media. This book was released on 2012-08-07 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents advances in matrix and tensor data processing in the domain of signal, image and information processing. The theoretical mathematical approaches are discusses in the context of potential applications in sensor and cognitive systems engineering. The topics and application include Information Geometry, Differential Geometry of structured Matrix, Positive Definite Matrix, Covariance Matrix, Sensors (Electromagnetic Fields, Acoustic sensors) and Applications in Cognitive systems, in particular Data Mining.

Download or read book Elements of Noncommutative Geometry written by Jose M. Gracia-Bondia and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Curves and Their Jacobians written by David Mumford and published by . This book was released on 1978 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Spectral Theory of Toeplitz Operators AM 99 Volume 99 written by L. Boutet de Monvel and published by Princeton University Press. This book was released on 2016-03-02 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations. If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol. It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the "quantized" objects associated with functions on compact contact manifolds.

Download or read book Jordan Algebras in Analysis Operator Theory and Quantum Mechanics written by Harald Upmeier and published by American Mathematical Soc.. This book was released on 1987-01-01 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Introduction to Riemann Surfaces Algebraic Curves and Moduli Spaces written by Martin Schlichenmaier and published by Springer. This book was released on 1989-01-11 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture is intended as an introduction to the mathematical concepts of algebraic and analytic geometry. It is addressed primarily to theoretical physicists, in particular those working in string theories. The author gives a very clear exposition of the main theorems, introducing the necessary concepts by lucid examples, and shows how to work with the methods of algebraic geometry. As an example he presents the Krichever-Novikov construction of algebras of Virasaro type. The book will be welcomed by many researchers as an overview of an important branch of mathematics, a collection of useful formulae and an excellent guide to the more extensive mathematical literature.

Download or read book Jordan Pairs written by O.G. Loos and published by Springer. This book was released on 2006-11-14 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Groups and Geometric Analysis written by Sigurdur Helgason and published by American Mathematical Society. This book was released on 2022-03-17 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group. The introductory chapter is a self-contained account of the analysis on surfaces of constant curvature. Later chapters cover general cases of the Radon transform, spherical functions, invariant operators, compact symmetric spaces and other topics. This book, together with its companion volume, Geometric Analysis on Symmetric Spaces (AMS Mathematical Surveys and Monographs series, vol. 39, 1994), has become the standard text for this approach to geometric analysis. Sigurdur Helgason was awarded the Steele Prize for outstanding mathematical exposition for Groups and Geometric Analysis and Differential Geometry, Lie Groups and Symmetric Spaces.

Download or read book Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem written by A. L. Carey and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolds. All conformal transformations sending the standard flat torsion-free quaternionic contact structure on the quaternionic Heisenberg group to a quaternionic contact structure with vanishing torsion of the Biquard connection are explicitly described. A "3-Hamiltonian form" of infinitesimal conformal automorphisms of quaternionic contact structures is presented.

Download or read book Prospects in Mathematics written by Hugo Rossi and published by American Mathematical Soc.. This book was released on with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: In celebration of Princeton University's 250th anniversary, the mathematics department held a conference entitled "Prospects in Mathematics". The purpose of the conference was to speculate on future directions of research in mathematics. This collection of articles provides a rich panorama of current mathematical activity in many research areas. From Gromov's lecture on quantitative differential topology to Witten's discussion of string theory, new ideas and techniques transfixed the audience of international mathematicians. The volume contains 11 articles by leading mathematicians, including historical presentations by J. Milnor and D. Spencer. It provides a guide to some of the most significant mathematical work of the past decade.

Download or read book Algebra Logic And Combinatorics written by Shaun Bullett and published by World Scientific. This book was released on 2016-04-21 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book leads readers from a basic foundation to an advanced level understanding of algebra, logic and combinatorics. Perfect for graduate or PhD mathematical-science students looking for help in understanding the fundamentals of the topic, it also explores more specific areas such as invariant theory of finite groups, model theory, and enumerative combinatorics.Algebra, Logic and Combinatorics is the third volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.

Download or read book Combinatorics of Finite Sets written by Ian Anderson and published by Courier Corporation. This book was released on 2002-01-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among other subjects explored are the Clements-Lindström extension of the Kruskal-Katona theorem to multisets and the Greene-Kleitmen result concerning k-saturated chain partitions of general partially ordered sets. Includes exercises and solutions.

Download or read book Differential Geometry and Symmetric Spaces written by and published by Academic Press. This book was released on 1962-01-01 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Geometry and Symmetric Spaces

Download or read book L2 Invariants Theory and Applications to Geometry and K Theory written by Wolfgang Lück and published by Springer Science & Business Media. This book was released on 2002-08-06 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.

Download or read book Partial Differential Relations written by Misha Gromov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical theory of partial differential equations is rooted in physics, where equations (are assumed to) describe the laws of nature. Law abiding functions, which satisfy such an equation, are very rare in the space of all admissible functions (regardless of a particular topology in a function space). Moreover, some additional (like initial or boundary) conditions often insure the uniqueness of solutions. The existence of these is usually established with some apriori estimates which locate a possible solution in a given function space. We deal in this book with a completely different class of partial differential equations (and more general relations) which arise in differential geometry rather than in physics. Our equations are, for the most part, undetermined (or, at least, behave like those) and their solutions are rather dense in spaces of functions. We solve and classify solutions of these equations by means of direct (and not so direct) geometric constructions. Our exposition is elementary and the proofs of the basic results are selfcontained. However, there is a number of examples and exercises (of variable difficulty), where the treatment of a particular equation requires a certain knowledge of pertinent facts in the surrounding field. The techniques we employ, though quite general, do not cover all geometrically interesting equations. The border of the unexplored territory is marked by a number of open questions throughout the book.