On the cone structure at infinity of Ricci flat manifolds with Euclidean volume growth and quadratic curvature decay.
Kähler-Einstein metrics and the generalized Futaki invariant.
Infinite geodesic rays in the space of Kähler potentials
In this paper we prove the existence of solutions of a degenerate complex Monge-Ampére equation on a complex manifold. Applying our existence result to a special degeneration of complex structure, we show how to associate to a change of complex structure an infinite length geodetic ray in the space of potentials. We also prove an existence result for the initial value problem for geodesics. We end this paper with a discussion of a list of open problems indicating how to relate our reults to the...
Hermitian curvature flow
We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler–Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler–Einstein metrics, and are automatically Kähler–Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existence and regularity results for this flow, as well as stability for the flow near Kähler–Einstein metrics...
Nonexistence of axially symmetric, stationary solution of Einstein vacuum equation with disconnected symmetric event horizon.
Complete Kähler manifolds with zero Ricci curvature. II.
Gauge theory and calibrated geometry. I.
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