Perspectives in Riemannian Geometry

Perspectives in Riemannian Geometry

Author: Vestislav Apostolov

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 264

ISBN-13: 0821838520

DOWNLOAD EBOOK

Special geometries as well as the relation between curvature and topology have always been of interest to differential geometers. More recently, these topics have turned out to be of use in physical problems related to string theory as well. This volume provides a unique and thorough survey on the latest developments on Riemannian geometry, special geometrical structures on manifolds, and their interactions with other fields such as mathematical physics, complex analysis, andalgebraic geometry. This volume presents ten papers written by participants of the ``Short Program on Riemannian Geometry,'' a workshop held at the CRM in Montreal in 2004. It will be a valuable reference for graduate students and research mathematicians alike. Information for our distributors: Titles inthis series are copublished with the Centre de Recherches Mathematiques.


Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition

Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition

Author:

Publisher: ScholarlyEditions

Published: 2013-05-01

Total Pages: 1227

ISBN-13: 1490107495

DOWNLOAD EBOOK

Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Random Structures and Algorithms. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Random Structures and Algorithms in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.


AdS/CFT Correspondence

AdS/CFT Correspondence

Author: Olivier Biquard

Publisher: European Mathematical Society

Published: 2005

Total Pages: 264

ISBN-13: 9783037190135

DOWNLOAD EBOOK

Since its discovery in 1997 by Maldacena, AdS/CFT correspondence has become one of the prime subjects of interest in string theory, as well as one of the main meeting points between theoretical physics and mathematics. On the physical side, it provides a duality between a theory of quantum gravity and a field theory. The mathematical counterpart is the relation between Einstein metrics and their conformal boundaries. The correspondence has been intensively studied, and a lot of progress emerged from the confrontation of viewpoints between mathematics and physics. Written by leading experts and directed at research mathematicians and theoretical physicists as well as graduate students, this volume gives an overview of this important area both in theoretical physics and in mathematics. It contains survey articles giving a broad overview of the subject and of the main questions, as well as more specialized articles providing new insight both on the Riemannian side and on the Lorentzian side of the theory.


Complex Analysis and Dynamical Systems IV

Complex Analysis and Dynamical Systems IV

Author: Mark Lʹvovich Agranovskiĭ

Publisher: American Mathematical Soc.

Published: 2011

Total Pages: 314

ISBN-13: 0821851977

DOWNLOAD EBOOK

The papers in this volume cover a wide variety of topics in differential geometry, general relativity, and partial differential equations. In addition, there are several articles dealing with various aspects of Lie groups and mathematics physics. Taken together, the articles provide the reader with a panorama of activity in general relativity and partial differential equations, drawn by a number of leading figures in the field. The companion volume (Contemporary Mathematics, Volume 553) is devoted to function theory and optimization.


Geometric Complex Analysis

Geometric Complex Analysis

Author: Jisoo Byun

Publisher: Springer

Published: 2018-09-08

Total Pages: 359

ISBN-13: 9811316724

DOWNLOAD EBOOK

The KSCV Symposium, the Korean Conference on Several Complex Variables, started in 1997 in an effort to promote the study of complex analysis and geometry. Since then, the conference met semi-regularly for about 10 years and then settled on being held biannually. The sixth and tenth conferences were held in 2002 and 2014 as satellite conferences to the Beijing International Congress of Mathematicians (ICM) and the Seoul ICM, respectively. The purpose of the KSCV Symposium is to organize the research talks of many leading scholars in the world, to provide an opportunity for communication, and to promote new researchers in this field.


Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds

Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds

Author: Raphael Ponge

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 150

ISBN-13: 0821841483

DOWNLOAD EBOOK

This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner andTaylor.


Toroidal Dehn Fillings on Hyperbolic 3-Manifolds

Toroidal Dehn Fillings on Hyperbolic 3-Manifolds

Author: Cameron Gordon

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 154

ISBN-13: 082184167X

DOWNLOAD EBOOK

The authors determine all hyperbolic $3$-manifolds $M$ admitting two toroidal Dehn fillings at distance $4$ or $5$. They show that if $M$ is a hyperbolic $3$-manifold with a torus boundary component $T 0$, and $r,s$ are two slopes on $T 0$ with $\Delta(r,s) = 4$ or $5$ such that $M(r)$ and $M(s)$ both contain an essential torus, then $M$ is either one of $14$ specific manifolds $M i$, or obtained from $M 1, M 2, M 3$ or $M {14}$ by attaching a solid torus to $\partial M i - T 0$.All the manifolds $M i$ are hyperbolic, and the authors show that only the first three can be embedded into $S3$. As a consequence, this leads to a complete classification of all hyperbolic knots in $S3$ admitting two toroidal surgeries with distance at least $4$.


Eigenvalues and Completeness for Regular and Simply Irregular Two-Point Differential Operators

Eigenvalues and Completeness for Regular and Simply Irregular Two-Point Differential Operators

Author: John Locker

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 194

ISBN-13: 0821841718

DOWNLOAD EBOOK

In this monograph the author develops the spectral theory for an $n$th order two-point differential operator $L$ in the Hilbert space $L2[0,1]$, where $L$ is determined by an $n$th order formal differential operator $\ell$ having variable coefficients and by $n$ linearly independent boundary values $B 1, \ldots, B n$. Using the Birkhoff approximate solutions of the differential equation $(\rhon I - \ell)u = 0$, the differential operator $L$ is classified as belonging to one of threepossible classes: regular, simply irregular, or degenerate irregular. For the regular and simply irregular classes, the author develops asymptotic expansions of solutions of the differential equation $(\rhon I - \ell)u = 0$, constructs the characteristic determinant and Green's function,characterizes the eigenvalues and the corresponding algebraic multiplicities and ascents, and shows that the generalized eigenfunctions of $L$ are complete in $L2[0,1]$. He also gives examples of degenerate irregular differential operators illustrating some of the unusual features of this class.


Operator Valued Hardy Spaces

Operator Valued Hardy Spaces

Author: Tao Mei

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 78

ISBN-13: 0821839802

DOWNLOAD EBOOK

The author gives a systematic study of the Hardy spaces of functions with values in the noncommutative $Lp$-spaces associated with a semifinite von Neumann algebra $\mathcal{M .$ This is motivated by matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), as well as by the recent development of noncommutative martingale inequalities. in this paper noncommutative Hardy spaces are defined by noncommutative Lusin integral function, and it isproved that they are equivalent to those defined by noncommutative Littlewood-Paley G-functions. The main results of this paper include: (i) The analogue in the author's setting of the classical Fefferman duality theorem between $\mathcal{H 1$ and $\mathrm{BMO $. (ii) The atomic decomposition of theauthor's noncommutative $\mathcal{H 1.$ (iii) The equivalence between the norms of the noncommutative Hardy spaces and of the noncommutative $Lp$-spaces $(1