Having completed a heuristic derivation of the monotonicity of Perelman reduced volume (Conjecture 1 from the previous lecture), we now turn to a rigorous proof. 3,157 more words

## Tags » Variation Formulae

#### 285G, Lecture 1: Flows on Riemannian manifolds

In the first lecture, we introduce *flows* on Riemannian manifolds , which are recipes for describing smooth deformations of such manifolds over time, and derive the basic… 3,749 more words