10 citations · 18 across the 4 of their papers we have counts for
5 papers · 1 filter
On stability and the convergence of the Kähler-Ricci flow
D. H. Phong, Jacob Sturm
Assuming uniform bounds for the curvature, the exponential convergence of the Kähler-Ricci flow is established under two conditions which are a form of stability: the Mabuchi energ…
On the Kähler-Ricci flow on complex surfaces
D. H. Phong, Jacob Sturm
It is observed that for complex surfaces, the positivity of the Ricci curvature is preserved by the Kähler-Ricci flow, under the additional assumption that the sum of the two lowes…
The Futaki invariant and the Mabuchi energy of a complete intersection
D. H. Phong, Jacob Sturm
We study the Futaki invariant and the Mabuchi K-energy of a Kähler manifold using the Deligne pairing technique developed in earlier papers. We first prove a rather simple char…
Scalar curvature, moment maps and the Deligne Pairing
D. H. Phong, Jacob Sturm
In this paper, we the improve the bound for the moment map derivative proved by Donaldson in his recent proof of the Hilbert-Mumford stability of complex manifolds with constant sc…
Stability, energy functionals, and Kähler-Einstein metrics
D. H. Phong, Jacob Sturm
An explicit seminorm $||f||_{#}$ on the vector space of Chow vectors of projective varieties is introduced, and shown to be a generalized Mabuchi energy functional for Chow varieti…