An Introduction to the Theory of Wave Maps and Related by Dan-Andrei Geba,Manoussos G Grillakis
By Dan-Andrei Geba,Manoussos G Grillakis
The wave maps method is without doubt one of the most lovely and hard nonlinear hyperbolic platforms, which has captured the eye of mathematicians for greater than thirty years now. within the examine of its a variety of matters, resembling the well-posedness idea, the formation of singularities, and the steadiness of the solitons, with a view to receive optimum effects, one has to exploit difficult instruments coming not just from research, but additionally from geometry and topology. furthermore, the wave maps process is not anything except the Euler–Lagrange procedure for the nonlinear sigma version, that's one of many primary difficulties in classical box theory.
One of the pursuits of our ebook is to provide an updated and virtually self-contained assessment of the most regularity effects proved for wave maps.
Another one is to introduce, to a large mathematical viewers, bodily influenced generalizations of the wave maps procedure (e.g., the Skyrme model), that are tremendous fascinating and hard of their personal right.
Read Online or Download An Introduction to the Theory of Wave Maps and Related Geometric Problems PDF
Best geometry & topology books
Topology is a huge topic with many branches extensively classified as algebraic topology, point-set topology, and geometric topology. Point-set topology is the most language for a wide number of mathematical disciplines. Algebraic topology serves as a strong software for learning the issues in geometry and diverse different parts of arithmetic.
The first target of this 2003 ebook is to provide a quick advent to the most principles of algebraic and geometric invariant concept. It assumes just a minimum historical past in algebraic geometry, algebra and illustration conception. subject matters lined comprise the symbolic process for computation of invariants at the house of homogeneous varieties, the matter of finite-generatedness of the algebra of invariants, the idea of covariants and buildings of express and geometric quotients.
Minkowski geometry is one of those non-Euclidean geometry in a finite variety of dimensions during which distance isn't really 'uniform' in all instructions. This e-book provides the 1st accomplished remedy of Minkowski geometry because the Nineteen Forties. the writer starts off by means of describing the basic metric homes and the topological houses of life of Minkowski house.
Effortless Topology: A Combinatorial and Algebraic method makes a speciality of the appliance of algebraic how to topological techniques and theorems. The book first elaborates on a few examples of surfaces and their classifications. Discussions specialise in combinatorial invariants of a floor, combinatorial equivalence, surfaces and their equations, topological surfaces, coordinates on a sphere and torus, and homes of the sector and torus.
- Meine Lieblings-Fraktale (German Edition)
- Topological and Bivariant K-Theory: 36 (Oberwolfach Seminars)
- Turning Points in the History of Mathematics (Compact Textbooks in Mathematics)
- 5000 Years of Geometry: Mathematics in History and Culture
Additional resources for An Introduction to the Theory of Wave Maps and Related Geometric Problems