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Course# MATH-731: Topics in geometric analysis I

Summary

The subject deals with differential geometry and its relation to global analysis, partial differential equations, geometric measure theory and variational principles to name a few.

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Related concepts (19)

Riemannian geometry

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner product on the tang

Poincaré conjecture

In the mathematical field of geometric topology, the Poincaré conjecture (UKˈpwæ̃kæreɪ, USˌpwæ̃kɑːˈreɪ, pwɛ̃kaʁe) is a theorem about the characterization of the 3-sphere, which is the hypersphere th

Partial differential equation

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function.
The function is often thought of as

Differential geometry

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus

Hodge theory

In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations. The key observation is that, giv