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.


Research supported in part by grants from the National Science Foundation, and by a Simons Fellowship in Mathematics.