Series: Lecture Notes in Mathematics, Vol. 2053
2012, 2012, Approx. 120 p.
Softcover Information
Softcover
ISBN 978-3-642-29845-5
Due: July 31, 2012
This book is intended for advanced students and young researchers interested in the analysis of partial differential equations and differential geometry. It discusses elementary concepts of surface geometry in higher-dimensional Euclidean spaces, in particular the differential equations of Gauss-Weingarten together with various integrability conditions and corresponding surface curvatures. It includes a chapter on curvature estimates for such surfaces, and, using results from potential theory and harmonic analysis, it addresses geometric and analytic methods to establish the existence and regularity of Coulomb frames in their normal bundles, which arise as critical points for a functional of total torsion.
Content Level â Graduate
Keywords â 53A07, 53A10, 35J15, 35J47, 30G20. - curvature estimates - elementary differential geometry - normal Coulomb frames - twodimensional surfaces in Euclidean spaces
Related subjects â Analysis - Dynamical Systems & Differential Equations - Geometry & Topology
Table of contents
Surface Geometry.- Elliptic Systems.- Normal Coulomb Frames in R4.- Normal Coulomb Frames in Rn+2
Series: Trends in Mathematics
2012, 2012, XII, 418 p. 4 illus. in color.
Hardcover
ISBN 978-3-0348-0447-9
Due: August 31, 2012
The Bialowieza workshops on Geometric Methods in Physics are among the most important meetings in the field. Every year some 80 to 100 participants from both mathematics and physics join to discuss new developments and to interchange ideas. This volume contains contributions by selected speakers at the XXX meeting in 2011 as well as additional review articles and shows that the workshop remains at the cutting edge of ongoing research.
The 2011 workshop focussed on the works of the late Felix A. Berezin (1931?1980) on the occasion of his 80th anniversary as well as on Bogdan Mielnik and Stanis?aw Lech Woronowicz on their 75th and 70th birthday, respectively. The groundbreaking work of Berezin is discussed from todayfs perspective by presenting an overview of his ideas and their impact on further developments. He was, among other fields, active in representation theory, general concepts of quantization and coherent states, supersymmetry and supermanifolds.
Another focus lies on the accomplishments of Bogdan Mielnik and Stanis?aw Lech Woronowicz. Mielnikfs apophatic approach to the description of quantum mixed states, the method of quantum state manipulation and their important implications for quantum computing and quantum entanglement are discussed as well as the intricacies of the quantum time operator. Woronowiczf fruitful notion of a compact quantum group and related topics are also addressed.
Content Level â Research
Keywords â Berezin quantization - coherent states - geometric quantization - mathematical physics - quantum groups - quantum states - superspaces
Related subjects â Algebra - Analysis
Series: Progress in Mathematics, Vol. 301
2012, 2012, Approx. 330 p.
Hardcover
ISBN 978-3-0348-0453-0
Due: August 31, 2012
Evolution equations of hyperbolic or more general p-evolution type form an active field of current research. This volume aims to collect some recent advances in the area in order to allow a quick overview of ongoing research. The contributors are first rate mathematicians. This collection of research papers is centred around parametrix constructions and microlocal analysis; asymptotic constructions of solutions; energy and dispersive estimates; and associated spectral transforms. Applications concerning elasticity and general relativity complement the volume. The book gives an overview of a variety of ongoing current research in the field and, therefore, allows researchers as well as students to grasp new aspects and broaden their understanding of the area. ?
Content Level â Research
Keywords â Schrodinger equations - generalized functions - hyperbolic equations - partial differential equations - pseudo-differential operators
Related subjects â Analysis - Dynamical Systems & Differential Equations - Mathematics
208pp (approx.) Pub. date: Jun 2012
ISBN: 978-1-84816-858-9
This book is a unique exposition of rich and inspiring geometries associated with Mobius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL(2,R). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, with the approach based on the Erlangen program of F Klein ? who defined geometry as a study of invariants under a transitive group action.
The treatment of elliptic, parabolic and hyperbolic Mobius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers. They form three potential commutative associative two-dimensional algebras, which are in perfect correspondences with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered.
Readership: Undergraduate and graduate students in geometry and algebra.
Erlangen Programme: Introduction
Groups and Homogeneous Spaces
Homogeneous Spaces from the Group SL(2,R)
Fillmore?Springer?Cnops Construction
Metric Invariants in Upper Half-Planes
Global Geometry of Upper Half-Planes
Conformal Unit Disk
Geodesics
Unitary Rotations
Series on Knots and Everything - Vol. 50
600pp (approx.) Pub. date: Jun 2012
ISBN: 978-981-4401-30-2
The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in the 1950s?1960s. The partition of these papers among the volumes is rather conditional. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated gsingular homologies of fiber spaces.h
Readership: Researchers in algebraic topology, its applications, and history of topology.
Singular Homology of Fiber Spaces (J-P Serre)
Homotopy Groups and Classes of Abelian Groups (J-P Serre)
Cohomology Modulo 2 of Eilenberg?MacLane Complexes (J-P Serre)
On Cohomology of Principal Fiber Bundles and Homogeneous Spaces of Compact Lie Groups (A Borel)
Cohomology Mod 2 of Some Homogeneous Spaces (A Borel)
The Steenrod Algebra and Its Dual (J Milnor)
On the Structure and Applications of the Steenrod Algebra (J F Adams)
Vector Bundles and Homogeneous Spaces (M F Atyah and F Hirzebruch)
The Methods of Algebraic Topology from Viewpoint of Cobordism Theory (S P Novikov)