Huai-Dong Cao

On locally conformally flat gradient steady Ricci solitons

In this paper, we classify n-dimensional (n>2) complete noncompact locally conformally flat gradient steady solitons. In particular, we prove that a complete noncompact non-flat conformally flat gradient steady Ricci soliton is, up to scaling, the Bryant soliton.

RECENT DEVELOPMENTS ON THE RICCI FLOW

This article reports recent developments of the research on Hamiltons Ricci flow and its applications.

On Bach-flat gradient shrinking Ricci solitons

In this paper, we classify n-dimensional (n>3) complete Bach-flat gradient shrinking Ricci solitons. More precisely, we prove that any 4-dimensional Bach-flat gradient shrinking Ricci soliton is either Einstein, or locally conformally flat hence a finite quotient of the Gaussian shrinking soliton

The Kähler–Ricci Flow on Fano Manifolds

R^4

On quantum de Rham cohomology theory

or the round cylinder

Martin compactification of a complete surface with negative curvature

S^3\times R

A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow

. More generally, for n>4, a Bach-flat gradient shrinking Ricci soliton is either Einstein, or a finite quotient of the Gaussian shrinking soliton

Recent Progress on Ricci Solitons

R^n

On complete gradient shrinking Ricci solitons

or the product

The structure of stable minimal hypersurfaces in

N^{n-1}\times R