Deals with Backlund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory. This book contains original contributions that represent various developments in the theory and applications of these transformations.
There have been many wonderful developments in the theory of minimal surfaces and geometric measure theory. This book covers variational geometry. It focuses on Plateau's Problem, which is concerned with surfaces that model the behavior of soap films.
Professor Atiyah is one of the greatest living mathematicians. He is a recipient of the Fields Medal, the mathematical equivalent of the Nobel... Læs mere
Deals with the theory of pairs of compact convex sets. This book also talks about the problem of finding different types of minimal representants of a pair of nonempty compact convex subsets of a locally convex vector space in the sense of the Radstrom-Hormander Theory.
Comprehensive coverage of the foundations, applications, recent developments, and future of conformal differential geometry. "Conformal Differential Geometry and Its Generalizations" systematically presents the foundations and manifestations of conformal differential geometry.
Contains research and expository papers on advances in foliations and Riemannian geometry. This work covers topics including: topology, geometry, dynamics and analysis of foliations, curvature, submanifold theory, Lie groups and harmonic maps.
The author describes harmonic maps which are critical points of the energy functional, and biharmonic maps which are critical points of the bienergy functional. Also given are fundamental materials of the variational methods in differential geometry, and
Presents an introduction to differential geometry. This book then introduces Lie groups and Lie algebras. It concludes with the... Læs mere
These texts contain 29 articles that cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics
Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory.