Kategoria BISAC: Mathematics >> Geometry - Differential

The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes (hence fibred products, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Frechet modules paralleling the useful...

The three-volume treatise consists of the volumes Minimal Surfaces (GL 339), Regularity of Minimal Surfaces (GL 340), and Glolbal Theory of Minimal Surfaces (GL 341) that replace the monograph Minimal Surfaces I, II, published as volumes 295 and 296 of the Grundlehren der mathematischen Wissenschaft series.

Ther first volume covers the classical theory as well as existence results concerning boundary value problems for minimal surfaces, in particular results for Plateau's problem.

The second volume deals with basic regularity results for minimal...

Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities a la Painleve, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations....

The book covers topics in the theory of algebraic transformation groups and algebraic varieties which are very much at the frontier of mathematical research.

This book develops a modern presentation of Continuum Mechanics, oriented towards numerical applications in the fields of nonlinear analysis of solids, structures and fluid mechanics. The kinematics of the continuum deformation, including pull-back / push-forward transformations between different configurations, stress and strain measures, balance principles, constitutive relations and variational principles are developed using general curvilinear coordinates. Even though the mathematical presentation of the different topics is quite rigorous, an effort is made to link formal developments...

In inverse problems, the aim is to obtain, via a mathematical model, information on quantities that are not directly observable but rather depend on other observable quantities. Inverse problems are encountered in such diverse areas of application as medical imaging, remote sensing, material testing, geosciences and financing. It has become evident that new ideas coming from differential geometry and modern analysis are needed to tackle even some of the most classical inverse problems. This book contains a collection of presentations, written by leading specialists, aiming to give the...

The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spacetime cannot be fundamentally correct. Hence there should exist a broader theory comprising both in appropriate limits, i.e., quantum gravity. This book gives readers a comprehensive introduction accessible to interested non-experts to the main issues surrounding the search for quantum gravity. These issues relate to fundamental questions...