Global Analysis

Global Analysis is a branch of mathematics that focuses on the study of the behavior and properties of functions and differential equations on a global scale, rather than just locally. It examines how global structures, such as boundaries and singularities, affect mathematical objects. In particular, it investigates the qualitative behavior of solutions to differential equations, often using tools from topology, geometry, and functional analysis. Global Analysis encompasses various topics, including the study of manifolds, differential operators, and spectral theory, with applications in physics, engineering, and other fields. The goal is to understand how global features influence local phenomena and vice versa.