Ben Weinkove - Research


My research is in geometric analysis. I work mostly in complex geometry, with an emphasis on Kähler-Einstein metrics and constant scalar curvature metrics, the Kähler-Ricci flow, the complex Monge-Ampère equation on manifolds and its generalizations.

Publications and preprints

V. Tosatti and B. Weinkove, The complex Monge-Ampère equation on compact Hermitian manifolds, preprint, arXiv
V. Tosatti and B. Weinkove, Estimates for the complex Monge-Ampère equation on Hermitian and balanced manifolds, preprint, arXiv
V. Tosatti and B. Weinkove, The Calabi-Yau equation on the Kodaira-Thurston manifold, preprint, arXiv
J. Song and B. Weinkove, The Kähler-Ricci flow on Hirzebruch surfaces, preprint, arXiv
V. Tosatti and B. Weinkove, The Calabi-Yau equation, symplectic forms and almost complex structures, preprint, arXiv
D.H. Phong, J. Song, J. Sturm, B. Weinkove, The modified Kähler-Ricci flow and solitons, preprint, arXiv
D.H. Phong, J. Song, J. Sturm, B. Weinkove, The Kähler-Ricci flow with positive bisectional curvature, Invent. Math. 173 (2008), no. 3, 651--665, arXiv
D.H. Phong, J. Song, J. Sturm, B. Weinkove, The Kähler-Ricci flow and the $\overline{\partial}$ operator on vector fields, J. Differential Geometry 81 (2009), 631--647, arXiv
J. Song, B. Weinkove,  Constructions of Kähler-Einstein metrics with negative scalar curvature, preprint, arXiv
V. Tosatti, B. Weinkove, S.-T. Yau, Taming symplectic forms and the Calabi-Yau equation, Proc. London Math. Soc. 97 (2008), no.2, 401--424, arXiv
V. Tosatti, B. Weinkove, The Calabi flow with small initial energy, Math. Res. Lett. 14 (2007), no. 6, 1033--1039, arXiv
D.H. Phong, J. Song, J. Sturm, B. Weinkove, The Moser-Trudinger inequality on Kähler-Einstein manifolds, Amer. J. Math. 130 (2008), no. 4, 1067--1085, arXiv
J. Song, B. Weinkove, On the convergence and singularities of the J-flow with applications to the Mabuchi energy, Comm. Pure Appl. Math. 61 (2008), no. 2, 210--229, arXiv
B. Weinkove, The Calabi-Yau equation on almost-Kähler four-manifolds, J. Differential Geometry 76 (2007), 317--349, arXiv
J. Song, B. Weinkove, Energy functionals and canonical Kähler metrics, Duke Math. J. 137 (2007), no. 1, 159--184, arXiv
J. Song, B. Weinkove, On Donaldson's flow of surfaces in a hyperkähler four-manifold, Math. Z. 256 (2007), no. 4, 769--787, arXiv
B. Weinkove, A complex Frobenius theorem, multiplier ideal sheaves and Hermitian-Einstein metrics on stable bundles, Trans. Amer. Math. Soc.  359  (2007),  no. 4, 1577--1592, arXiv
B. Weinkove, On the J-flow in higher dimensions and the lower boundedness of the Mabuchi energy, J. Differential Geom.  73  (2006),  no. 2, 351--358, arXiv
B. Weinkove, Convergence of the J-flow on Kähler surfaces, Comm. Anal. Geom.  12  (2004),  no. 4, 949--965, arXiv
B. Weinkove, Singularity formation in the Yang-Mills flow, Calc. Var. Partial Differential Equations  19  (2004),  no. 2, 211--220, arXiv