Natasa Sesum

BOUNDING SCALAR CURVATURE AND DIAMETER ALONG THE KÄHLER RICCI FLOW (AFTER PERELMAN)

In this short note we present a result of Perelman with detailed proof. The result states that if

Ricci flow on surfaces with conic singularities

g(t)

On the extinction profile of solutions to fast diffusion

is the Kahler Ricci flow on a compact, Kahler manifold

Linear and dynamical stability of Ricci-flat metrics

M

Eternal solutions to the Ricci flow on ℝ2

with

The mean curvature at the first singular time of the mean curvature flow

c_1(M)>0

Ricci flow on three-dimensional manifolds with symmetry

, the scalar curvature and diameter of

Ricci flow on asymptotically conical surfaces with nontrivial topology

(M,g(t))

Convergence of Kähler-Einstein orbifolds

stay uniformly bounded along the flow, for

Blow-up of the mean curvature at the first singular time of the mean curvature flow

t\in[0,\infty)