Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced by Guoying Jiang in 1986. The book presents an overview of the importa...
Geometry and Dynamics of Groups and Spaces (Progress in Mathematics, #265)
Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
The book provides a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image construction and reconstruction. The self-contained survey chapters, written by leading mathematicians, engineers, and computer scientists, present cutting-edge research and results in the field. Three main areas are covered: theoretical results, algorithms, and practical applications. Following an historical and introductory overview of the field, the b...
Aspects of Differential Geometry I (Synthesis Lectures on Mathematics and Statistics)
by Peter Gilkey, Jeonghyeong Park, and Ramon Vazquez-Lorenzo
Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. In Book I, we focus on preliminaries. Chapter 1 provides an introduction to multivariable calculus and treats the Inverse Function Theorem, Implicit Function Theorem, the theory of the Riemann Integral, and the Change of Variable Theorem. Chapter 2 treats smooth manifolds, the tangent and cotangent bund...
Foliation theory has its origins in the global analysis of solutions of ordinary differential equations: on an n-dimensional manifold M, an [autonomous] differential equation is defined by a vector field X; if this vector field has no singularities, then its trajectories form a par- tition of M into curves, i.e. a foliation of codimension n - 1. More generally, a foliation F of codimension q on M corresponds to a partition of M into immersed submanifolds [the leaves] of dimension ,--------,- - ....
This research monograph mainly discusses a canonical and explicit compactification of the moduli spaces of abelian varieties, K3 surfaces and compact hyperKahler varieties. For that, we use two theories of compactification - Satake compactifications for locally symmetric spaces in terms of the Lie theory, and Morgan-Shalen compactifications of complex varieties in terms of valuations. We show they coincide for Shimura varieties. The obtained compactifications are no longer varieties but we pro...
Geometry, Lie Theory and Applications (Abel Symposia, #16)
This book consists of contributions from the participants of the Abel Symposium 2019 held in Ålesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity. The chapters are written...
200 Worksheets - Greater Than for 8 Digit Numbers (200 Days Math Greater Than, #8)
by Kapoo Stem
The Theory of Lie Derivatives and Its Applications
by Kentaro Yano
Theory of Moduli (C.I.M.E. Foundation Subseries, #1337) (Lecture Notes in Mathematics, #1337)
The contributions making up this volume are expanded versions of the courses given at the C.I.M.E. Summer School on the Theory of Moduli.
Tight Polyhedral Submanifolds and Tight Triangulations (Lecture Notes in Mathematics, #1612)
by Wolfgang Kuhnel
This volume is an introduction and a monograph about tight polyhedra. The treatment of the 2-dimensional case is self- contained and fairly elementary. It would be suitable also for undergraduate seminars. Particular emphasis is given to the interplay of various special disciplines, such as geometry, elementary topology, combinatorics and convex polytopes in a way not found in other books. A typical result relates tight submanifolds to combinatorial properties of their convex hulls. The chapters...
The Modern Geometry (Graduate Texts in Mathematics, v. 93)
by B. A. Dubrovin, etc., A.T. Fomenko, and S. P. Novikov
This is the first volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This material is explained in as simple and concrete a language as possible, in a terminology acceptable to physicists. The text for the second edition has been substantially revised.
Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfangen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen fur die historische wie auch die disziplingeschichtliche Forschung zur Verfugung, die jeweils im historischen Kontext betrachtet werden mussen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
Lectures on Differential Geometry (EMS Series of Lectures in Mathematics)
by Iskander A. Taimanov
Geometric Analysis (Lecture Notes in Mathematics, #2263) (C.I.M.E. Foundation Subseries, #2263)
by Ailana Fraser, Andre Neves, Peter M. Topping, and Paul C. Yang
This book covers recent advances in several important areas of geometric analysis including extremal eigenvalue problems, mini-max methods in minimal surfaces, CR geometry in dimension three, and the Ricci flow and Ricci limit spaces. An output of the CIME Summer School "Geometric Analysis" held in Cetraro in 2018, it offers a collection of lecture notes prepared by Ailana Fraser (UBC), André Neves (Chicago), Peter M. Topping (Warwick), and Paul C. Yang (Princeton). These notes will be a valua...
The main purpose of this monograph is to give an elementary and self-contained account of the existence of asymptotically hyperbolic Einstein metrics with prescribed conformal infinities sufficiently close to that of a given asymptotically hyperbolic Einstein metric with non positive curvature. The proof is based on an elementary derivation of sharp Fredholm theorems for self-adjoint geometric linear elliptic operators on asymptotically hyperbolic manifolds.
This book treats that part of Riemannian geometry related to more classical topics in a very original, clear and solid style. The author successfully combines the co-ordinate and invariant approaches to differential geometry, giving the reader tools for practical calculations as well as a theoretical understanding of the subject.
The Index Theorem for Minimal Surfaces of Higher Genus (Memoirs of the American Mathematical Society)
Mathematicians working in global analysis and/or minimal surface theory.
This work is intended for graduate students and research mathematicians interested in differential geometry and partial differential equations.
Geometry of Incompatible Deformations (de Gruyter Studies in Mathematical Physics, #50)
This monograph provides a systematic treatment of differential geometry in modeling of incompatible fiite deformations in solids. Included are discussions of generalized deformations and stress measures on smooth manifolds, geometrical formalizations for structurally inhomogeneous bodies, representations for configurational forces, and evolution equations.
This book aims to bridge the gap between probability and differential geometry. It gives two constructions of Brownian motion on a Riemannian manifold: an extrinsic one where the manifold is realized as an embedded sub manifold of Euclidean space and an intrinsic one based on the 'rolling' map. It is then shown how geometric quantities (such as curvature) are reflected by the behavior of Brownian paths and how that behavior can be used to extract information about geometric quantities. Readers s...
Integrable Systems, Geometry, and Topology (AMS/IP Studies in Advanced Mathematics)
The articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems. The article by Burstall gives a beautiful exposition on isothermic surfaces and their relations to in...
Selected Works of Isadore Singer: Volume 1
by Daniel S. Freed and John Lott
This collection presents the major mathematical works of Isadore Singer, selected by Singer himself, and organized thematically into three volumes:1. Functional analysis, differential geometry and eigenvalues2. Index theory3. Gauge theory and physics Each volume begins with a commentary (and in the first volume, a short biography of Singer), and then presents the works on its theme in roughly chronological order.