Comprehensive coverage of the foundations, applications, recent developments, and future of conformal differential geometry Conformal Differential Geometry and Its Generalizations is the first and only text that systematically presents the foundations and manifestations of conformal differential geometry.
Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets.
This volume is a compilation of papers presented at the conference on differential geometry, in particular, minimal surfaces, real hypersurfaces of a non-flat complex space form, submanifolds of symmetric spaces and curve theory.
This book deals with the classical theory of Nevanlinna on the value distribution of meromorphic functions of one complex variable, based on minimum prerequisites for complex manifolds.
This volume presents the results and problems in several complex variables especially L2-methods, Riemannian and Hermitian geometry, spectral theory in Hilbert space, probability and applications in mathematical physics.
In the Teichmuller theory of Riemann surfaces, besides the classical theory of quasi-conformal mappings, vari- ous approaches from differential geometry and algebraic geometry have merged in recent years.
This volume is devoted to the "e;hyperbolic theory"e; of dynamical systems (DS), that is, the theory of smooth DS's with hyperbolic behaviour of the tra- jectories (generally speaking, not the individual trajectories, but trajectories filling out more or less "e;significant"e; subsets in the phase space.
Based on a two-semester course aimed at illustrating various interactions of "e;pure mathematics"e; with other sciences, such as hydrodynamics, thermodynamics, statistical physics and information theory, this text unifies three general topics of analysis and physics, which are as follows: the dimensional analysis of physical quantities, which contains various applications including Kolmogorov's model for turbulence; functions of very large number of variables and the principle of concentration along with the non-linear law of large numbers, the geometric meaning of the Gauss and Maxwell distributions, and the Kotelnikov-Shannon theorem; and, finally, classical thermodynamics and contact geometry, which covers two main principles of thermodynamics in the language of differential forms, contact distributions, the Frobenius theorem and the Carnot-Caratheodory metric.
This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) manifolds, without using differential calculus.
Starting from an undergraduate level, this book systematically develops the basics of* Calculus on manifolds, vector bundles, vector fields and differential forms,* Lie groups and Lie group actions,* Linear symplectic algebra and symplectic geometry,* Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory.
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory.
The discoveries of the past decade have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology.
The general theory of relativity, as formulated by Albert Einstein in 1915, provided an astoundingly original perspective on the physical nature of gr- itation, showing that it could be understood as a feature of a curvature in the four-dimensional continuum of space-time.
This book offers a detailed exploration of the intrinsic geometrical properties of warped product spaces through the lens of mathematical analysis and global differential geometry.
This book is a collection of papers in memory of Gu Chaohao on the subjects of Differential Geometry, Partial Differential Equations and Mathematical Physics that Gu Chaohao made great contributions to with all his intelligence during his lifetime.
This volume is a compilation of new results and surveys on the current state of some aspects of the foliation theory presented during the conference "e;FOLIATIONS 2012"e;.
A synthetic approach to intrinsic differential geometry in the large and its connections with the foundations of geometry was presented in "e;The Geometry of Geodesics"e; (1955, quoted as G).
This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc.
This textbook offers a rigorous introduction to the foundations of Riemannian Geometry, with a detailed treatment of homogeneous and symmetric spaces, as well as the foundations of the General Theory of Relativity.
Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics.
