Extending Calabi’s conjecture to complete noncompact Kähler manifolds which are asymptotically n , n > 2

Philippe Delanoë

Compositio Mathematica (1990)

  • Volume: 75, Issue: 2, page 219-230
  • ISSN: 0010-437X

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Delanoë, Philippe. "Extending Calabi’s conjecture to complete noncompact Kähler manifolds which are asymptotically $\mathbb {C}^n$, $n &gt; 2$." Compositio Mathematica 75.2 (1990): 219-230. <http://eudml.org/doc/90035>.

@article{Delanoë1990,
author = {Delanoë, Philippe},
journal = {Compositio Mathematica},
keywords = {Monge-Ampère operator; Ricci curvature; Calabi's conjecture; Kähler asymptotically -manifolds},
language = {eng},
number = {2},
pages = {219-230},
publisher = {Kluwer Academic Publishers},
title = {Extending Calabi’s conjecture to complete noncompact Kähler manifolds which are asymptotically $\mathbb \{C\}^n$, $n &gt; 2$},
url = {http://eudml.org/doc/90035},
volume = {75},
year = {1990},
}

TY - JOUR
AU - Delanoë, Philippe
TI - Extending Calabi’s conjecture to complete noncompact Kähler manifolds which are asymptotically $\mathbb {C}^n$, $n &gt; 2$
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 75
IS - 2
SP - 219
EP - 230
LA - eng
KW - Monge-Ampère operator; Ricci curvature; Calabi's conjecture; Kähler asymptotically -manifolds
UR - http://eudml.org/doc/90035
ER -

References

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  1. 1 R.L. Bishop and S.I. Goldberg, On the second cohomology group of a Kähler manifold of positive curvature, Proc. Amer. Math. Soc.16 (1965), 119-122. Zbl0125.39403MR172221
  2. 2 E. Calabi, The space of Kähler metrics, Proc. Internat. Congress Math. Amsterdam (1954), vol. 2, 206-207. 
  3. 3 E. Calabi, A construction of nonhomogeneous Einstein metrics, Proc. Amer. Math. Soc.27 (1975), 17-24. Zbl0309.53043MR379912
  4. 4 A. Chaljub-Simon and Y. Choquet-Bruhat, Problèmes elliptiques du second ordre sur une variété euclidienne à l'infini, Ann. Fac. Sc. Toulouse1 (1978), 9-25. Zbl0411.35044MR533596
  5. 5 P. Delanoë, Analyse asymptotiquement euclidienne de l'opérateur de Monge-Ampère réel, preprint Nice (1988). 
  6. 6 P. Delanoë, Partial decay on simple manifolds, Preprint Université de Nice (1990). Zbl0714.35027MR1172619
  7. 7 P. Delanoë, Local inversion of elliptic problems on compact manifolds, to appear in Mathematica Japonica, Vol. 35 (1990). Zbl0717.35025MR1067866
  8. 8 P. Delanoë, Obstruction to prescribed positive Ricci curvature, to appear in Pacific J. Math. Zbl0676.53050MR1091527
  9. 9 G. de Rham, Variétés différentiables, HermannParis (1960), Actualités Sc. et Industr. 1222. Zbl0089.08105
  10. 10 D DeTurck, Metrics with prescribed Ricci curvature, Seminar on Differential Geometry, Edit. S. T. Yau, Annals of Math. St. 102, Princeton Univ. Press (1982), 525-537. Zbl0478.53031MR645758
  11. 11 D DeTurck and N. Koiso, Uniqueness and non-existence of metrics with prescribed Ricci curvature, Ann. I. H. P. Anal. non lin.1 (1984), 351-359. Zbl0556.53026MR779873
  12. 12 A. Jeune, Un analogue du théorème de Calabi-Yau sur Cn, n &gt; 2, Preprint (1990). 
  13. 13 J.L. Kazdan, Prescribing the curvature of a Riemannian manifold, Amer. Math. Soc. CBMS Regional Conf.57 (1985). Zbl0561.53048MR787227
  14. 14 K. Kodaira, Harmonic fields in Riemannian geometry (generalized potential theory), Ann. of Math.50 (1949), 587-665. Zbl0034.20502MR31148
  15. 15 K. Kodaira and J. Morrow, Complex manifolds, Holt Rinehart & Winston (1971). Zbl0325.32001MR302937
  16. 16 A. Lichnerowicz, Théories relativistes de la gravitation et de l'électromagnétisme, Masson, Paris (1955). Zbl0065.20704
  17. 17 R. Lockhart, Fredholm, Hodge and Liouville theorems on noncompact manifolds, Trans. Amer. Math. Soc.301 (1987), 1-35. Zbl0623.58019MR879560
  18. 18 N. Mok, Y.-T. Siu and S.-T. Yau, The Poincaré-Lelong equation on complete Kähler manifolds, Compositio Math. 44 (1981), 183-218. Zbl0531.32007MR662462
  19. 19 R. Schoen and S.-T. Yau, Complete three dimensional manifolds with positive Ricci and scalar curvature, Seminar on Differential Geometry, Edit. S.T. Yau, Annals of Math. St. 102, Princeton Univ. Press (1982), 209-228. Zbl0481.53036MR645740
  20. 20 S.-T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation, I, Comm. Pure Appl. Math.XXXI (1978), 339-411. Zbl0369.53059MR480350

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