SUNY at Stony Brook SUNY at Stony Brook SUNY at Stony Brook

Research Articles by

Claude LeBrun

  1. H-Space with a Cosmological Constant, Proc. R. Soc. London A 380 (1982) 171--185.
  2. The First Formal Neighbourhood of Ambitwistor Space for Curved Space-Time, Lett. Math. Phys. 6 (1982) 345--354.
  3. Spaces of Complex Null Geodesics in Complex-Riemannian Geometry,Trans. Am. Math. Soc. 278 (1983) 209--231.
  4. Twistor CR Manifolds and Three-Dimensional Conformal Geometry, Trans. Am. Math. Soc. 284 (1984) 601--616.
  5. Ambitwistors and Einstein's equations, Class. Quant. Grav. 2 (1985) 555--563.
  6. Foliated CR Manifolds, J. Diff. Geom. 22 (1985) 81--96.
  7. (with M.G. Eastwood) Thickenings and Supersymmetric Extensions of Complex Manifolds, Am. J. Math. 108 (1986) 1177--1192.
  8. On the Topology of Self-Dual 4-Manifolds, Proc. Am. Math. Soc. 98 (1986) 637--640.
  9. Thickenings and Gauge Fields, Class. Quant. Grav. 3 (1986) 1039--1059.
  10. Orthogonal Complex Structures on S6, Proc. Am. Math. Soc. 101 (1987) 136--138.
  11. Poon's Self-Dual Metrics and Kähler Geometry, J. Diff. Geom. 28 (1988) 341--343.
  12. A Rigidity Theorem for Quaternionic-Kähler Manifolds, Proc. Am. Math. Soc. 103 (1988) 1205--1208.
  13. (with M. Rothstein) Moduli of Super Riemann Surfaces, Comm. Math. Phys. 117 (1988) 159--176.
  14. Counter-Examples to the Generalized Positive Action Conjecture, Comm. Math. Phys. 118 (1988) 591--596.
  15. Quaternionic-Kähler Manifolds and Conformal Geometry, Math. Ann. 284 (1989) 353--376.
  16. (with M. Anderson and P. Kronheimer) Complete Ricci-Flat Kähler Manifolds of Infinite Topological Type, Comm. Math. Phys. 125 (1989) 637--642.
  17. (with Y.-S. Poon and R.O. Wells, Jr.) Projective Embeddings of Complex Supermanifolds, Comm. Math. Phys. 126 (1990) 433--452.
  18. Ambitwistors and Conformal Gravity, NATO Adv. Sci. Inst. Ser. B Phys. 245 (1990) 621--632.
  19. Twistors, Ambitwistors, and Conformal Gravity, in Twistors in Mathematics and Physics,
    LMS Lecture Notes 156, Bailey & Baston, editors, Cambridge University Press, 1990, pp. 71--86.
  20. Complete Ricci-Flat Kähler Metrics on Cn Need Not Be Flat, Proc. Symp. Pure Math. 52.2 (1991) 297--304.
  21. Thickenings and Conformal Gravity, Comm. Math. Phys. 139 (1991) 1--43.
  22. Explicit Self-Dual Metrics on CP2 # ... # CP2, J. Diff. Geom. 34 (1991) 223--253.
  23. Anti-Self-Dual Hermitian Metrics on Blown-Up Hopf Surfaces, Math. Ann. 289 (1991) 383--392.
  24. Scalar-Flat Kähler Metrics on Blown-Up Ruled Surfaces, J. reine angew. Math. 420 (1991) 161--177.
  25. On Complete Quaternionic-Kähler Manifolds, Duke Math. J. 63 (1991) 723--743.
  26. (with M.G. Eastwood) Fattening Complex Manifolds: Curvature and Kodaira-Spencer Maps, J. Geom. Phys. 8 (1992) 123--146.
  27. Twistors, Kähler Manifolds, and Bimeromorphic Geometry I, J. Am. Math. Soc. 5 (1992) 289--316.
  28. (with Y.-S. Poon) Twistors, Kähler Manifolds, and Bimeromorphic Geometry II, J. Am. Math. Soc. 5 (1992) 317--325.
  29. (with Y.-S. Poon) Self-Dual Manifolds with Symmetry, Proc. Symp. Pure Math. 54 (1993) 365--377.
  30. (with M.A. Singer) Existence and Deformation Theory for Scalar-Flat Kähler Metrics on Compact Complex Surfaces, Inv. Math. 112 (1993) 273--313.
  31. Self-Dual Manifolds and Hyperbolic Geometry, in Einstein Manifolds and Yang-Mills Connections,
    LNPAM 145, T. Mabuchi and S. Mukai, editors, Marcel Dekker, 1993, pp. 99--131.
  32. A Kähler Structure on the Space of String World-Sheets, Class. Quant. Grav. 10 (1993) L141-L148.
  33. A Finiteness Theorem for Quaternionic-Kähler Manifolds with Positive Scalar Curvature, Contemp. Math. 154 (1993) 89--101.
  34. (with S.R. Simanca) Extremal Kähler Metrics and Complex Deformation Theory, Geom. Func. Analysis 4 (1994) 298--336.
  35. (with S.R. Simanca) On the Kähler Classes of Extremal Metrics, in Geometry and Global Analysis,
    Kotake, Nishikawa & Schoen, editors, Tohoku University, 1994, pp. 255--271.
  36. (with S.M. Salamon) Strong Rigidity of Positive Quaternion-Kähler Manifolds, Inv. Math. 118 (1994) 109--132.
  37. (with M.A. Singer) A Kummer-type Construction of Self-Dual 4-Manifolds, Math. Ann. 300 (1994) 165--180.
  38. Anti-Self-Dual Riemannian 4-Manifolds, in Twistor Theory, LNPAM 169, Stephen Huggett, editor, Marcel Dekker, 1995, pp. 81--94.
  39. Einstein Metrics and Mostow Rigidity, Math. Res. Lett. 2 (1995) 1--8.
  40. (with S.R. Simanca) On Kähler Surfaces of Constant Positive Scalar Curvature, J. Geom. Analysis 5 (1995) 115--127.
  41. Fano Manifolds, Contact Structures, and Quaternionic Geometry, Int. J. Math. 3 (1995) 419--437.
  42. Anti-Self-Dual Metrics and Kähler Geometry, Proc. Int. Cong. Math. 1994, vol. 1, , Birkhäuser, 1995, pp. 498--507.
  43. On the Scalar Curvature of Complex Surfaces, Geom. Func. An. 5 (1995) 619--628.
  44. Polarized 4-Manifolds, Extremal Kähler Metrics, and Seiberg-Witten Theory, Math. Res. Lett. 2 (1995) 653-662.
  45. Four-Manifolds without Einstein Metrics, Math. Res. Lett. 3 (1996) 133--147.
  46. Einstein Metrics on Complex Surfaces, in Geometry and Physics, LNPAM 184, Anderson, Dupont, Pedersen & Swann, editors, Marcel Dekker, 1997, pp. 167--176.
  47. (with S. Nayatani and T. Nitta) Self-Dual Manifolds with Positive Ricci Curvature, Math. Z. 224 (1997) 49-63.
  48. (with J.-S. Kim and M. Pontecorvo) Scalar-Flat Kähler Surfaces of All Genera, J. reine angew. Math. 486 (1997) 69--95.
  49. Yamabe Constants and the Perturbed Seiberg-Witten Equations, Comm. An. Geom. 5 (1997) 535--553.
  50. Twistors for Tourists: A Pocket Guide for Algebraic Geometers, Proc. Symp. Pure Math. 62.2 (1997) 361--385.
  51. On the Notion of General Type, Rendiconti Mat. Roma 17 (1997) 513--522.
  52. (with F. Catanese) On the Scalar Curvature of Einstein Manifolds, Math. Res. Lett. 4 (1997) 843--854.
  53. On Four-Dimensional Einstein Manifolds, in The Geometric Universe: Science, Geometry, and the Work of Roger Penrose,
    Huggett, Mason, Tod, Tsou & Woodhouse, editors, Oxford University Press, 1998, pp. 81--98.
  54. (with M. Gursky) Yamabe Invariants and Spinc Structures, Geom. Func. An. 8 (1998) 965--977.
  55. Weyl Curvature, Einstein Metrics, and Seiberg-Witten Theory, Math. Res. Lett. 5 (1998) 423--438.
  56. Kodaira Dimension and the Yamabe Problem, Comm. An. Geom. 7 (1999) 133--156.
  57. (with M. Gursky) On Einstein Manifolds of Positive Sectional Curvature, Ann. Glob. An. Geom. 17 (1999) 315--328.
  58. Topology versus Chern Numbers for Complex 3-Folds, Pac. J. Math. 191 (1999) 123--131.
  59. Four-Dimensional Einstein Manifolds, and Beyond, in Surveys in Differential Geometry, vol VI:
    Essays on Einstein Manifolds, C. LeBrun & M. Wang, editors, International Press of Boston, 1999, pp. 247--285.
  60. Einstein Metrics and the Yamabe Problem, in Trends in Mathematical Physics, V. Alexiades & G. Siopsis, editors, AMS/IP, 1999, pp. 353--376.
  61. Diffeomorphisms, Symplectic Forms, and Kodaira Fibrations, Geom. Top. 4 (2000) 451--456.
  62. Curvature and Smooth Topology in Dimension Four, Séminaires et Congrès 4 (2000) 179--200.
  63. Ricci Curvature, Minimal Volumes, and Seiberg-Witten Theory, Invent. Math. 145 (2001) 279--316.
  64. (with M. Ishida) Spin Manifolds, Einstein Metrics, and Differential Topology, Math. Res. Lett. 9 (2002) 229--240.
  65. Hyperbolic Manifolds, Harmonic Forms, and Seiberg-Witten Invariants, Geom. Dedicata 91 (2002) 137--154.
  66. (with L.J. Mason) Zoll Manifolds and Complex Surfaces, J. Diff. Geom. 61 (2002) 453--535.
  67. Scalar Curvature, Covering Spaces, and Seiberg-Witten Theory, New York J. Math. 9 (2003) 93--97.
  68. (with M. Ishida) Curvature, Connected Sums, and Seiberg-Witten Theory, Comm. An. Geom. 11 (2003) 809--836.
  69. Einstein Metrics, Four-Manifolds, and Differential Topology, in Surveys in Differential Geometry, vol. VIII:
    Papers in Honor of Calabi, Lawson, Siu, and Uhlenbeck, S.-T. Yau, editor, International Press of Boston, 2003, pp. 235--255.
  70. Curvature Functionals, Optimal Metrics, and the Differential Topology of 4-Manifolds, in Different Faces of Geometry,
    S.K. Donaldson, Y. Eliashberg & M. Gromov, editors, Kluwer Academic/Plenum, 2004, pp. 199--256.
  71. Einstein Metrics, Symplectic Minimality, and Pseudo-Holomorphic Curves, Ann. Glob. An. Geom. 28 (2005) 157--177.
  72. Twistors, Holomorphic Disks, and Riemann Surfaces with Boundary, in Perspectives in Riemannian Geometry,
    V. Apostolov, A. Dancer, N. Hitchin & M. Wang, editors, American Mathematical Society, 2006, pp. 209--221.
  73. (with L.J. Mason) Nonlinear Gravitons, Null Geodesics, and Holomorphic Disks, Duke Math. J. 136 (2007) 205--273.
  74. (with K. Akutagawa and M. Ishida) Perelman's Invariant, Ricci Flow, and the Yamabe Invariants of Smooth Manifolds, Arch. Math. 88 (2007) 71--76.
  75. (with X.X. Chen and B. Weber) On Conformally Kähler, Einstein Manifolds, J. Am. Math. Soc. 21 (2008) 1137-1168.
  76. (with B. Maskit) On Optimal 4-Dimensional Metrics, J. Geom. Analysis 18 (2008) 537-564.
  77. Four-Manifolds, Curvature Bounds, and Convex Geometry, in Riemannian Topology and Geometric Structures on Manifolds,
    K. Galicki & S.R. Simanca, editors, Birkhäuser, 2009, pp. 119--152.
  78. (with L.J. Mason) The Einstein-Weyl Equations, Scattering Maps, and Holomorphic Disks, Math. Res. Lett. 16 (2009) 291--301.
  79. Einstein Metrics, Complex Surfaces, and Symplectic 4-Manifolds, Math. Proc. Cambr. Phil. Soc. 147 (2009) 1--8.
  80. Einstein Metrics, Four-Manifolds, and Conformally Kähler Geometry, in Surveys in Differential Geometry, vol. XIII:
    Geometry, Analysis, and Algebraic Geometry: Forty Years of the Journal of Differential Geometry, Cao & Yau, editors, IP Boston, 2009, pp. 135--147.
  81. The Einstein-Maxwell Equations, Extremal Kähler Metrics, and Seiberg-Witten Theory, in The Many Facets of Geometry: a Tribute to Nigel Hitchin,
    Bourguignon, Garcia-Prada & Salamon, editors, Oxford University Press, 2010, pp. 17--33.
  82. (with L.J. Mason) Zoll Metrics, Branched Covers, and Holomorphic Disks, Comm. An. Geom. 18 (2010) 475--502.
  83. On Einstein, Hermitian 4-Manifolds, J. Diff. Geom. 90 (2012) 277-302.
  84. Einstein Manifolds and Extremal Kähler Metrics, J. reine angew. Math. 678 (2013) 69--94.
  85. Calabi Energies of Extremal Toric Surfaces, in Surveys in Differential Geometry, vol. XVIII:
    Geometry and Topology, Cao & Yau, editors, International Press of Boston, 2013, pp. 195--226.
  86. (with M.F. Atiyah) Curvature, Cones, and Characteristic Numbers, Math. Proc. Cambr. Phil. Soc. 155 (2013) 13--37.
  87. The Einstein-Maxwell Equations, Kähler Metrics, and Hermitian Geometry, J. Geom. Phys 91 (2015) 163--171.
  88. Einstein Metrics, Harmonic Forms, and Symplectic Four-Manifolds, Ann. Global An. Geom. 48 (2015) 75--85.
  89. Weyl Curvature, Del Pezzo Surfaces, and Almost-Kähler Geometry, J. Geom. Analysis 25 (2015) 1744--1772.
  90. Edges, Orbifolds, and Seiberg-Witten Theory, J. Math. Soc. Japan 67 (2015) 979--1021.
  91. The Einstein-Maxwell Equations and Conformally Kähler Geometry, Comm. Math. Phys. 344 (2016) 621--653.
  92. (With H.-J. Hein) Mass in Kähler Geometry, Comm. Math. Phys. 347 (2016) 183--221.
  93. Twistors, Hyper-Kähler Manifolds, and Complex Moduli, in Special Metrics and Groups Actions in Geometry,
    Chiossi, Fino, Musso, Podestà & Vezzoni, editors, Springer, 2017, pp. 207--214.
  94. Mass, Kähler Manifolds, and Symplectic Geometry, Ann. Global An. Geom. 56 (2019) 97--112.
  95. Bach-Flat Kähler Surfaces, J. Geom. Analysis 30 (2020) 2491--2514 .
  96. (with C.J. Bishop) Anti-Self-Dual 4-Manifolds, Quasi-Fuchsian Groups, & Almost-Kähler Geometry, Comm. An. Geom. 28 (2020) 745-780.
  97. Einstein Metrics, Harmonic Forms, and Conformally Kähler Geometry, in Differential Geometry in the Large, LMS Lecture Notes 463,
    Dearricott, Tuschmann, Nikolayevsky, Leistner, & Crowley, editors, Cambridge University Press, 2021, pp. 214--240.
  98. Einstein Manifolds, Self-Dual Weyl Curvature, and Conformally Kähler Geometry, Math. Res. Lett. 28 (2021) 127-144.
  99. Einstein Manifolds, Conformal Curvature, and Anti-Holomorphic Involutions, Ann. Math. Qué. 45(2) (2021) 391-405.
  100. Twistors, Self-Duality, and Spinc Structures, SIGMA 17 (2021) 102, 11 pages.
  101. The Scalar Curvature of 4-Manifolds, in Perspectives in Scalar Curvature, vol. 1, M. Gromov & H. B. Lawson, eds, World Scientific, 2023, pp. 643-707.
  102. Yamabe Invariants, Homogeneous Spaces, and Rational Complex Surfaces, SIGMA 19 (2023) 027, 11 pages.
  103. Curvature in the Balance: The Weyl Functional and Scalar Curvature of 4-Manifolds, Pure Appl. Math. Q. 19 (2023) 2737-2763.
  104. (with M. Albanese) Kodaira Dimension and the Yamabe Problem, II, Comm. An. Geom. 31(2023) 2387-2411.
  105. (With O. Biquard and P. Gauduchon) Gravitational Instantons, Weyl Curvature, and Conformally Kähler Geometry, Int. Math. Res. Not. IMRN (2024) 13295-13311.
  106. Einstein Constants and Smooth Topology, e-print arXiv:2502.10560 [math.DG]; to appear in Real and Complex Geometry: in Honour of Paul Gauduchon, edited by Liviu Ornea, Springer, 2025.

Simons Foundation
Research supported in part by fourteen successive grants from the National Science Foundation, and by two Simons Fellowships in Mathematics.