mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, global analysis, also called analysis on manifolds, is the study of the global and topological properties of differential equations on manifolds and

vector bundle In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to eve ...

s. Global analysis uses techniques in infinite-dimensional manifold theory and topological spaces of mappings to classify behaviors of differential equations, particularly nonlinear differential equations. These spaces can include singularities and hence catastrophe theory is a part of global analysis. Optimization problems, such as finding geodesics on

Riemannian manifold In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined. Euclidean space, the N-sphere, n-sphere, hyperbolic space, and smooth surf ...

s, can be solved using differential equations, so that the calculus of variations overlaps with global analysis. Global analysis finds application in

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

in the study of dynamical systems and topological quantum field theory.

Journals

* Annals of Global Analysis and Geometry * The Journal of Geometric Analysis

Journals

See also

References

Further reading