Peter M. Topping

On type-I singularities in Ricci flow

We dene several notions of singular set for Type I Ricci ows and show that they all coincide. In order to do this, we prove that blow-ups around singular points converge to nontrivial gradient shrinking solitons, thus extending work of Naber [15]. As a byproduct we conclude that the volume of a nite-volume singular set vanishes at the singular time. We also dene a notion of density for Type I Ricci ows and use it to prove a regularity theorem reminiscent of White’s partial regularity result for mean curvature ow [22].

RICCI FLOW, ENTROPY AND OPTIMAL TRANSPORTATION

Let a smooth family of Riemannian metrics

Reverse Bubbling and Nonuniqueness in the Harmonic Map Flow

g(\tau)

Relating diameter and mean curvature for submanifolds of Euclidean space

satisfy the backwards Ricci flow equation on a compact oriented

L-optimal transportation for Ricci flow

n

Existence of Ricci Flows of Incomplete Surfaces

-dimensional manifold

Decay estimates for Rivière’s equation, with applications to regularity and compactness

M

Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics

. Suppose two families of normalized

Flowing maps to minimal surfaces

n

Local monotonicity and mean value formulas for evolving Riemannian manifolds

-forms