papers.htlm
Preprints of Latest Work
- Formal structure of scalar curvature in generalized Kahler geometry
(with J. Streets, Y. Ustinovskiy)
arXiv:2404.14595
- Hamiltonian 2-forms and new explicit Calabi-Yau metrics and gradient steady Kahler-Ricci solitons on ℂn
(with C. Cifarelli)
arXiv:2305.15626
- The Riemannian and symplectic geometry of the space of generalized Kahler structures
(with J. Streets, Y. Ustinovskiy)
arXiv:2302.07314
- The generalized Kahler Calabi-Yau problem
(with X. Fu,
J. Streets, Y. Ustinovskiy),
arXiv:2211.09104
Research Articles in International Journals
- Weighted K-stability and coercivity with applications to extremal Kahler and Sasaki metrics
(with S. Jubert ,
A. Lahdili)
Geometry & Topology 8 (2023), 3229-3302,
arXiv:2104.09709
- Twisted differentials and Lee classes of locally conformally symplectic complex surfaces (with
G. Dloussky)
Math. Z. 303 (2023), Article 76.
arXiv:2204.02122
- Variational structure and uniqueness of generalized Kahler-Ricci solitons
(with
J. Streets, Y. Ustinovskiy)
Peking Mathematical Journal 6 (2023), 307-351.
arXiv:2109.10295
- Generalized Kaehler-Ricci flow on toric Fano varieties
(with
J. Streets, Y. Ustinovskiy)
Trans. Amer. Math. Soc. 375 (2022), 4369-4409.
arXiv:2104.03268
- Weighted extremal Kahler metrics and the Einstein-Maxwell geometry of projective bundles (with
G. Maschler and C.W.Tonnesen-Friedman),
Comm. Anal. Geom. 30 (2022), 689-744, arXiv:1808.02813
- Weighted K-stability of polarized varieties and extremality of Sasaki manifolds
(with D.M.J.Calderbank, E.Legendre),
Advances in Math. 391 (2021), Paper No 107969,
arXiv:2012.08628
- The nondegenerate generalized Kaehler Calabi-Yau problem (with
J. Streets),
J. Reine Angew. Math. 777 (2021), 1-48
,
arXiv:1703.08650
- The CR geometry of weighted extremal Kahler and Sasaki metrics (with D.M.J.Calderbank),
Math. Ann. 379 (2021), 1047-1088,
arXiv:1810.10618
- Extremal Kaehler Poincare type metrics on toric varieties (with
H. Auvray, L. Sektnan),
J. Geom. Anal. 31 (2021), 1223-1290,
arXiv:1711.08424
- Levi-Kahler reduction of CR structures, products of spheres, and toric geometry (with D.M.J.Calderbank,
P. Gauduchon, E.Legendre),
Math. Res. Lett., 27 (2020), 1565-1629, arXiv:1708.05253
- Toric contact geometry in arbitrary codimension (with D.M.J.Calderbank,
P. Gauduchon, E.Legendre ),
Int. Math. Res. Notices (IMRN) 2020, 2436-2467, arXiv:1708.04952
- Relative K-polystability of projective bundles over a curve (with
J. Keller),
Trans. Amer. Math. Soc. 372 (2019), 233-266,
arXiv:1701.08507
- Conformally Kaehler, Einstein-Maxwell Geometry (with
G. Maschler),
J. Eur. Math. Soc (JEMS) 21 (2019), 1319-1360,
arXiv:1512.06391
- On the Lee classes of locally conformally symplectic complex surfaces (with
G. Dloussky),
Journal Symplectic Geom. 16 (2018), 931-958,
arXiv:1611.00074
- ALE scalar-flat Kaehler metrics on non-compact weighted projective spaces (with
Y. Rollin ),
Math. Ann. 367 (2017), 1685-1726,
arXiv:1510.02226
- Locally conformally symplectic structures on compact non-Kaehler complex surfaces (with
G. Dloussky),
Int. Math. Res. Notices (IMRN) 9 (2016), 2717-2747,
arXiv:1501.02687
- Ambitoric geometry I: Einstein metrics and extremal ambikaehler structures (with D.M.J.Calderbank,
P. Gauduchon),
J. Reine Angew. Math. 721 (2016), 109-147, arXiv:1302.6975
- Ambitoric geometry II: Extremal toric surfaces and Einstein 4-orbifolds (with D.M.J.Calderbank,
P. Gauduchon),
Ann. Sci. Ecole Norm. Supp. (4) 48 (2015), 1075-1112,
arXiv:1302.6979
- An extremal eigenvalue problem in Kaehler geometry (with
D. Jakobson, G. Kokarev),
J. Geom. Phys. 91 (2015), 108-116, Special issue dedicated to P. Gauduchon's 70th birthday,
arXiv:1411.7725
- From locally conformally Kaehler to bi-Hermitian structures on non-Kaehler complex surfaces (with
M. Bailey,
G. Dloussky),
Math. Res. Lett. 22 (2015), 317-336,
arXiv:1307.3660
- A splitting theorem for extremal Kaehler metrics
(with H. Huang),
J. Geom. Anal. 25 (2015), 149-170, arXiv:1212.3665
- Extremal Kaehler metrics on projective bundles over a curve, (with
D.M.J.Calderbank,
P.Gauduchon,
C.W.Tonnesen-Friedman),
Advances in Math. 227 (2011), 2385-2424, arXiv:0905.0498
- Bihermitian metrics on Hopf surfaces, (with G. Dloussky)
Math. Res. Lett. 15 (2008), 827-839,
arXiv:0710.2266
- Hamiltonian 2-forms in Kaehler geometry IV: Weakly Bochner-flat Kaehler
manifolds, (with D.M.J.Calderbank,
P.Gauduchon,
C.W.Tonnesen-Friedman),
Comm. Ann. Geom. 16 (2008), 91-126,
math.DG//0511119
- Hamiltonian 2-forms in Kaehler geometry III: Extremal metrics and stability, (with
D.M.J.Calderbank,
P.Gauduchon,
C.W.Tonnesen-Friedman),
Invent. Math. 173 (2008), 547-601,
math.DG/0511118
- Generalized Kaehler manifolds, commuting complex structures, and split tangent bundles,
(with M. Gualtieri),
Comm. Math. Phys. 271 (2007), 561-575, math.DG/0605342
- A remark on Kaehler metrics of constant scalar curvature on ruled complex surfaces,
(with C.W.Tonnesen-Friedman),
Bull. London Math. Soc. 38 (2006), 494-500,
math.DG/0411271
- Hamiltonian 2-forms in Kaehler Geometry I: General Theory,
(with D.M.J.Calderbank and
P.Gauduchon),
J. Differential Geom. 73 (2006), 359-412, math.DG/0202280
- Hamiltonian 2-forms in Kaehler Geometry II: Global Classification,
(with D.M.J.Calderbank,
P.Gauduchon,
C.W.Tonnesen-Friedman),
J. Differential Geom. 68 (2004), 277-345,
math.DG/0401320
- The odd-dimensional Goldberg conjecture,
(with T.Draghici and
A.Moroianu),
Math. Nachr. 279 (2006), 948-952, math.DG/030241
- Kaehler reduction of metrics with holonomy G_2, (with S.Salamon),
Comm. Math. Phys. 246 (2004), 43-61,
math.DG/0303197
- The geometry of weakly selfdual Kaehler surfaces,(with
D.M.J.Calderbank and
P.Gauduchon),
Compositio Math. 135 (2003), 279-322,
math.DG/0104233, authors comments
- Self-dual Einstein Hermitian 4-manifolds, (with P.Gauduchon),
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 1 (2002), 203-243,
[PDF]
- Local models and integrability of certain almost Kaehler 4-manifolds,
(with J. Armstrong and T.Draghici),
Math. Ann. 323 (2002),
633-666, math.DG/0109098
- Local rigidity of certain classes of almost Kaehler 4-manifolds, (with J. Armstrong and T.Draghici),
Ann. Glob. Anal. Geom. 21(2002), 151-176, math.DG/9911197
- A splitting theorem for Kaehler manifolds whose Ricci tensors have constant eigenvalues,
(with T.Draghici and
A.Moroianu),
Int. J. Math. 12 (2001), 769-789,
math.DG0007122
- Bihermitian surfaces with odd first Betti number,
Math. Z.
238 (2001), 555-568,
[PDF]
- Symplectic 4-manifolds with Hermitian Weyl tensor (with J. Armstrong),
Trans.
Amer. Math. Soc. 352 (2000), 4501-4513,
[PDF ]
- Almost-Kaehler 4-manifolds with J-invariant Ricci
tensor and special Weyl tensor, (with T.Draghici),
Q. J. Math.
51 (2000), 275-294, math.DG/9911196
- Compact Hermitian surfaces and isotropic curvature, (with J.Davidov),
Illinois J. Math. 44(2000), 438-451.
- An integrability theorem for almost Kaehler 4-manifolds, (with T.Draghici
and D.Kotschick),
C. R. Acad. Sci. Paris 329 (1999), 413-418,
[PDF]
- Weakly-Einstein Hermitian surfaces, (with O.Mushkarov),
Ann. Inst. Fourier (Grenoble) 49 (1999), 1673-1692,
[PDF]
- Bihermitian structures on complex surfaces,
(with P. Gauduchon and
G. Grantcharov),
Proc. London Math. Soc. 79 (1999), 414-429,
[PDF], Erratum
- Orthogonal complex structures on certain Riemannian
6-manifolds,
(with G. Grantcharov and S.Ivanov),
Diff. Geom. Appl. 11 (1999) 279-296, [PDF]
- Hermitian conformal classes and almost Kaehler structures on four
manifolds, (with T.Draghici),
Diff. Geom. Appl. 11 (1999) 179-195, [PDF]
- Hermitian structures on twistor spaces, (with G.Grantcharov
and S. Ivanov),
Ann. Glob. Anal. Geom. 16 (1998), 291-308, [PDF]
- Generalized Goldberg-Sachs theorems
for pseudo-Riemannian
four-manifolds,
J. Geom. Phys. 27 (1998), 185-198.
- The Riemannian
Goldberg-Sachs Theorem, (with P. Gauduchon),
Int. J. Math. 8 (1997), 421-439.
- Compact Hermitian surfaces of
constant antiholomorphic sectional curvature, (with G. Ganchev and S.Ivanov),
Proc. Amer. Math. Soc. 125 (1997), 3705-3714.
- Compact self-dual Hermitian surfaces, (with J.Davidov
and O.Mushkarov),
Trans. Amer. Math. Soc. 385 (1996), 3051-3063.
- Compact *-Einstein Hermitian
surfaces of negative type,
C. R. Acad. Sci. Bulgare 48
(1995), 19-22.
Other Publications
- The Kahler geometry of toric manifolds,
Lecture notes of a mini course at CIRM 2019,
arXiv:2208.12493
- Extremal Kaehler Metrics on Ruled Manifolds and Stability,
(with D.M.J.Calderbank,
P. Gauduchon,
C.W.Tonnesen-Friedman),
in ``Géométrie différentielle, physique mathématique, mathématiques et société (II),
Volume en l'honneur de Jean Pierre Bourguignon'',
O. Hijazi (éditeur), Astérsique 322 (2008),
[PDF]
- The curvature and the integrability of almost-Kaehler manifolds: A survey, (with T.Draghici),
in `Symplectic and Contact Topology: Interactions and Perspectives', eds. Y. Eliashberg, B. Khesin, F. Lalonde, Fields Institute Communications Series
35 , AMS (2003) pp. 25-49,
math.DG/0302152
- Geometry of Hermitian surfaces, (with J.Davidov, G. Grantcharov,
and O.Mushkarov),
in
`Topics in Complex Analysis, Differential Geometry and Mathematical
Physics, Proceedings St. Konstantin, 1996', eds. S. Dimiev and K.
Sekigawa, World Sci. Publishing River Edge, NJ (1997), pp. 94-104.
The papers here (and in math.DG) may differ in minor respects from the published articles.