PrerequisiteMulti-variable Calculus, Basic Partial Differential Equation, Basics of Riemannian Geometry(optional)AbstractThe course introduces hyperbolic partial differential equations and conservation laws from both historical and modern perspectives, focusing on important examples rather than general theory. The classical concepts such as characteristics and Riemann invariant plays an indispe...
IntroductionThis course is an introduction to the convergence and collapsing theory of Riemannian manifolds, which is an important tool in Riemannian geometry. We shall introduce the Gromov-Hausdorff distance and study the convergence theory of Riemannian manifolds with respect to this distance. We will discuss the collapsing theory of Riemannian manifolds with bounded sectional curvatures.Lect...