Ricci Lower Bound for Kähler–ricci Flow

On the lower bound of energy functional E1 (I) —a stability theorem on the Kähler Ricci flow

Non-kähler Ricci Flow Singularities That Converge to Kähler–ricci Solitons

We investigate Riemannian (non-Kähler) Ricci flow solutions that develop finite-time Type-I singularities with the property that parabolic rescalings at the singularities converge to singularity models taking the form of shrinking Kähler–Ricci solitons. More specifically, the singularity models for these solutions are given by the “blowdown soliton” discovered in [FIK03]. Our results support th...

A Note on Compact Kähler-ricci Flow with Positive Bisectional Curvature

We show that for any solution gij̄(t) to the Kähler-Ricci flow with positive bisectional curvature Rīijj̄(t) > 0 on a compact Kähler manifold M , the bisectional curvature has a uniform positive lower bound Rīijj̄(t) > C > 0. As a consequence, gij̄(t) converges exponentially fast in C ∞ to an KählerEinstein metric with positive bisectional curvature as t → ∞, provided we assume the Futaki-invariant...

A Property of Kähler-Ricci Solitons on Complete Complex Surfaces

where Rαβ(x, t) denotes the Ricci curvature tensor of the metric gαβ(x, t). One of the main problems in differential geometry is to find canonical structure on manifolds. The Ricci flow introduced by Hamilton [8] is an useful tool to approach such problems. For examples, Hamilton [10] and Chow [7] used the convergence of the Ricci flow to characterize the complex structures on compact Riemann s...

(kähler-)ricci Flow on (kähler) Manifolds

One of the most interesting questions in Riemannian geometry is that of deciding whether a manifold admits curvatures of certain kinds. More specifically, one might want to know whether some given manifold admits a canonical metric, i.e. one with constant curvature of some form (sectional curvature, scalar curvature, etc.). (This will in fact have many topological implications.). One such probl...