Publications and preprints

Lecture notes on the Kahler-Ricci flow

with B. Weinkove [pdf]

The Kahler-Ricci flow on projective bundles

with G. Szekelyhidi and B. Weinkove [arXiv]

Contracting exceptional divisors by the Kahler-Ricci flow II

with B. Weinkove [arXiv]

Metric flips with Calabi symmetry

with Y. Yuan [arXiv]

Finite time extinction of the Kahler-Ricci flow

[arXiv]

Contracting exceptional divisors by the Kahler-Ricci flow

with B. Weinkove [arXiv]

The Kahler-Ricci flow on singular Calabi-Yau varieties

with Y. Yuan

The Kahler-Ricci flow through singularities

with G. Tian [arXiv]

Test configurations, large deviations and geodesic rays on toric varieties

with S. Zelditch [arXiv]

The Kahler-Ricci flow on Hirzebruch surfaces

With B. Weinkove, to appear in Crelle’s Journal [arXiv]

Canonical measures and Kahler-Ricci flow

with G.Tian, to appear in J. Amer. Math. Soc. [arXiv]

On the convergence of the modified Kähler-Ricci flow and solitons

with D.H. Phong, J. Sturm and B. Weinkove, Comment. Math. Helv. 86 (2011), no. 1, 91-112 [arXiv]

Bergman metrics and geodesics in the space of Kahler metrics on toric varieties

with S. Zelditch, Anal. PDE. 3 (2010), no. 3, 295-358 [arXiv]

Constructions of Kahler-Einstein metrics with negative scalar curvature

with B. Weinkove, Math. Ann. 347 (2010), no. 1, 59-79 [arXiv]

The Kahler-Ricci flow with positive bisectional curvature

with D.H. Phong, J. Sturm and B. Weinkove, Invent. Math. 173 (2008), no. 3, 651-665 [arXiv]

The Kahler-Ricci flow and the \bar\partial operator on vector fields

with D.H. Phong, J. Sturm and B. Weinkove, J. Differential Geom. 81 (2008), no. 3, 631-647 [arXiv]

The Moser-Trudinger inequality on Kahler-Einstein manifolds

with D.H. Phong, J. Sturm and B. Weinkove, Amer. J. Math. 130 (2008), no. 4, 1067-1085 [arXiv]

The convergence and singularities of the J-flow with applications to the Mabuchi energy

with B. Weinkove, Comm. Pure Appl. Math. 61 (2008), no. 2, 210-229 [arXiv]

The Kahler-Ricci flow on minimal surfaces of positive Kodaira dimension

with G. Tian, Invent. Math. 170 (2007), no. 3, 609-653 [arXiv]

Energy functionals and canonical Kahler metrics

with B. Weinkove, Duke Math. J. 137 (2007), no. 1, 159-184 [arXiv]

Convergence of Bergman geodesics on CP^1

with S. Zelditch, Ann. Inst. Fourier, Grenoble 57, 7 (2007) 2209-2237 [arXiv]

On Donaldson's flow of surfaces in a hyperkahler four-manifold

with B. Weinkove, Math. Z. 256 (2007), no. 4, 769-787 [arXiv]

The Kahler-Ricci flow on Kahler surfaces

Proceedings of Gokova Geometry-Topology Conference 2006, 123-135

The α-invariant on toric Fano manifolds

Amer. J. Math. 127 (2005), no. 6, 1247-1259 [arXiv]

The α-invariant on certain surfaces with symmetry groups

Trans. Amer. Math. Soc. 357 (2005), 45-57 [arXiv]

The Szego kernel of an orbifold circle bundle and its application

Thesis at Columbia University, 2004 [arXiv]