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.

Lecture Notes

J. Song and B. Weinkove, Lecture Notes on the Kähler-Ricci flow, preliminary version, updated 11/21/11

Publications and preprints

  1. V. Tosatti and B. Weinkove, On the evolution of a Hermitian metric by its Chern-Ricci form, preprint, arXiv
  2. J. Song, G. Szekelyhidi and B. Weinkove, The Kähler-Ricci flow on projective bundles, preprint, arXiv
  3. M. Sherman and B. Weinkove, Interior derivative estimates for the Kähler-Ricci flow, preprint, arXiv
  4. J. Song and B. Weinkove, Contracting exceptional divisors by the Kähler-Ricci flow II, preprint, arXiv
  5. V. Tosatti and B. Weinkove, Plurisubharmonic functions and nef classes on complex manifolds, to appear in Proc. Amer. Math. Soc., arXiv
  6. J. Song and B. Weinkove, Contracting exceptional divisors by the Kähler-Ricci flow, preprint, arXiv
  7. V. Tosatti and B. Weinkove, The complex Monge-Ampère equation on compact Hermitian manifolds, J. Amer. Math. Soc. 23 (2010), no.4, 1187-1195,  arXiv
  8. V. Tosatti and B. Weinkove, Estimates for the complex Monge-Ampère equation on Hermitian and balanced manifolds, Asian J. Math. 14 (2010), no.1, 19-40,  arXiv
  9. V. Tosatti and B. Weinkove, The Calabi-Yau equation on the Kodaira-Thurston manifold, to appear in J. Inst. Math. Jussieu, arXiv
  10. J. Song and B. Weinkove, The Kähler-Ricci flow on Hirzebruch surfaces, to appear in Crelle's Journal, arXiv
  11. V. Tosatti and B. Weinkove, The Calabi-Yau equation, symplectic forms and almost complex structures, in Geometry and Analysis, Vol. I, 475-493, Advanced Lectures in Math. 17, International Press, 2010,  arXiv
  12. D.H. Phong, J. Song, J. Sturm and B. Weinkove, The modified Kähler-Ricci flow and solitons, to appear in Comment. Math. Helv., arXiv
  13. D.H. Phong, J. Song, J. Sturm and B. Weinkove, The Kähler-Ricci flow with positive bisectional curvature, Invent. Math. 173 (2008), no. 3, 651--665, arXiv
  14. D.H. Phong, J. Song, J. Sturm and B. Weinkove, The Kähler-Ricci flow and the $\overline{\partial}$ operator on vector fields, J. Differential Geometry 81 (2009), 631--647, arXiv
  15. J. Song and B. Weinkove,  Constructions of Kähler-Einstein metrics with negative scalar curvature, Math. Ann. 347 (2010), no. 1, 59--79, arXiv
  16. V. Tosatti, B. Weinkove and S.-T. Yau, Taming symplectic forms and the Calabi-Yau equation, Proc. London Math. Soc. 97 (2008), no.2, 401--424, arXiv
  17. V. Tosatti and B. Weinkove, The Calabi flow with small initial energy, Math. Res. Lett. 14 (2007), no. 6, 1033--1039, arXiv
  18. D.H. Phong, J. Song, J. Sturm and B. Weinkove, The Moser-Trudinger inequality on Kähler-Einstein manifolds, Amer. J. Math. 130 (2008), no. 4, 1067--1085, arXiv
  19. J. Song and 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
  20. B. Weinkove, The Calabi-Yau equation on almost-Kähler four-manifolds, J. Differential Geometry 76 (2007), 317--349, arXiv
  21. J. Song and B. Weinkove, Energy functionals and canonical Kähler metrics, Duke Math. J. 137 (2007), no. 1, 159--184, arXiv
  22. J. Song and B. Weinkove, On Donaldson's flow of surfaces in a hyperkähler four-manifold, Math. Z. 256 (2007), no. 4, 769--787, arXiv
  23. 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
  24. 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
  25. B. Weinkove, Convergence of the J-flow on Kähler surfaces, Comm. Anal. Geom.  12  (2004),  no. 4, 949--965, arXiv
  26. B. Weinkove, Singularity formation in the Yang-Mills flow, Calc. Var. Partial Differential Equations  19  (2004),  no. 2, 211--220, arXiv

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