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On the extension ofL 2 holomorphic functions III: negligible weights

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References

  1. Andreotti, A., Vesentini, E.: Sopra un teorema di Kodaira, Ann. Sci. Norm. Sup. Pisa15, 283–309 (1961)

    MATH  MathSciNet  Google Scholar 

  2. Andreotti, A., Vesentini, E.: Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Publ. Math. IHES25, 313–362 (1965)

    MATH  Google Scholar 

  3. Catlin, D.: Estimation of invartiant metrics on pseudoconvex domains of dimension two, Math. Z.200, 429–466 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  4. D’Angelo, J.: A note on the Bergman kernel, Duke Math. J.45, 259–265 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  5. Demailly, J.P.: EstimationsL 2 pour l’operateur d"d’un fibré vectoriel sem-positif au-dessus d’un variété kählerienne compléte, Ann. Sci. Ec. Norm. Super.15, 457–511 (1982)

    MATH  MathSciNet  Google Scholar 

  6. Demailly, J.P.: Regularization of closed positive currents and intersection theory, J. Alg. Geom.1, 361–409 (1992)

    MATH  MathSciNet  Google Scholar 

  7. Diederich, K., Fornaess, J.E.: Pseudoconvex domains with real analytic boundary, Ann. Math.107, 371–384 (1978)

    Article  MathSciNet  Google Scholar 

  8. Diederich, K., Herbort, G.: Geometric and analytic boundary invariants of pseudoconvex domains. Comparison results, J. Geom. Analysis3, 237–267 (1993)

    MATH  MathSciNet  Google Scholar 

  9. Diederich, K., Herbort, G., Ohsawa, T.: The Bergman kernel on uniformly extendable pseudoconvex domains, Math. Ann.273, 471–478 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  10. Diederich, K., Lieb, I.: Konvexität in der komplexen Analysis, DMV-Seminar 2 Birkhäuser-Verlag, 1981

  11. Diederich, K., Pflug, P.: Über Gebiete mit vollständiger Kähler metric, Math. Ann.257, 191–198 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  12. Donnelly, H., Fefferman, C.:L 2 cohomology and index theorem for the Bergman metric, Ann. Math.118, 593–618 (1983)

    Article  MathSciNet  Google Scholar 

  13. Fujiki, A., Nakano, S.: Supplement to ‘On the inverse of monoidal transformation’, Publ. RIMS7, 637–644 (1971-72)

    MathSciNet  Google Scholar 

  14. Gaffney, M.P.: A special Stokes’ theorem for complete Riemannian manifolds, Ann. of Math.60, 140–145 (1954)

    Article  MathSciNet  Google Scholar 

  15. Grauert, H.: Characterisierung der Holomorphiegebiete durch die vollständige Kählersche Metric, Math. Ann.131, 38–75 (1956)

    Article  MATH  MathSciNet  Google Scholar 

  16. Grauert, H.: On Levi’s problem and the imbedding of real-analytic manifolds, Ann. of Math.68, 460–472 (1958)

    Article  MathSciNet  Google Scholar 

  17. Greene, R.E., Wu, H.: Function theory on manifolds which possess a pole, Lecture Notes in Math. vol. 699, Springer-Verlag, Berlin-New York-Heidelberg, 1979

    MATH  Google Scholar 

  18. Gromov, M.: Kähler hyperbolicity andL 2-Hodge theory, J. Diff. Geom.33, 263–292 (1991)

    MATH  MathSciNet  Google Scholar 

  19. Herbort, G.: Logarithmic growth of the Bergman kernel for weakly pseudoconvex domains in ℂ3 of finite type, Manuscripta Math.45, 69–76 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  20. Herbort, G.: On the invariant differential metrics near pseudoconvex boundary points where the Levi form has corank one, Nagoya Math. J.130, 25–54 (1993)

    MATH  MathSciNet  Google Scholar 

  21. Hörmander, L.:L 2 estimates and existence theorems for the\(\bar \partial\)-operator, Acta Math.113, 89–152 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  22. Hörmander, L.: Complex Analysis in Several Variables, Princeton, D. van Nostrand 1966

    MATH  Google Scholar 

  23. Manivel, L., Un théorème de prolongmentL 2 de sections holomorphes d’un fibré hermitien, Math. Z.212, 107–122 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  24. McNeal, J.: Local geometry of decoupled pseudoconvex domains, Aspekte der Math.17, 223–230 (1990)

    Google Scholar 

  25. Mok, N., Yau, S.T.: Completeness of the Kähler-Einstein metric on bounded domains and the characterization of domains of holomorphy by curvature conditions, The mathematical heritage of Henri Poincaré, Part 1 (Bloomington, Ind., 1980), 41–59, Proc. Sympos. Pure Math.39, Amer. Math. Soc., Providence, R.I. 1983

    Google Scholar 

  26. Mok, N., Zhong, J.Q.: Compactifying complete Kähler-Einstein manifolds of finite topological type and bounded curvature, Ann. of Math.129, 427–470 (1989)

    Article  MathSciNet  Google Scholar 

  27. Nagel, A., Rosay, J.P., Stein, E.M., Wainger, S.: Estimates for the Bergman and Szegö kernels in ℂ2, Ann. of Math.129, 113–149 (1989)

    Article  MathSciNet  Google Scholar 

  28. Nakano, S.: On complex analytic vector bundles, J. Math. Soc. Japan7, 1–12 (1955)

    Article  MATH  MathSciNet  Google Scholar 

  29. Nakano, S.: On the inverse of monoidal transformation, Publ. RIMS, Kyoto Univ.6 483–502 (1970/71)

    MathSciNet  Google Scholar 

  30. Ohsawa, T.: On complete Kähler domains withC 1-boundary, Publ. RIMS, Kyoto Univ.16, 929–940 (1980)

    MATH  MathSciNet  Google Scholar 

  31. Ohsawa, T.: Vanishing theorems on complete Kähler manifolds, Publ. RIMS, Kyoto Univ.20, 21–38 (1984)

    MATH  MathSciNet  Google Scholar 

  32. Ohsawa, T.: Boundary behaviour of Bergman kernel function on pseudoconvex domains, Publ. RIMS, Kyoto Univ.20, 897–902 (1984)

    MATH  MathSciNet  Google Scholar 

  33. Ohsawa, T.: On the extension ofL 2 holomorphic functions II, Publ. RIMS, Kyoto Univ.24, 265–275 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  34. Ohsawa, T.: The existence of right inverses of residue homomorphisms, Complex Analysis and Geometry, 285–291, Plenum Press, New York and London, 1993

    Google Scholar 

  35. Ohsawa, T., Takegoshi, K.: On the extension ofL 2 holomorphic functions, Math. Z.195, 197–204 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  36. Oka, K.: Domaines finis sans point critique intérieur, Japan. J., Math.,27, 97–155 (1953)

    MathSciNet  Google Scholar 

  37. Siu, Y.T., Yau, S.T.: Complete Kähler manifolds with nonpositive curvature of faster than quadratique decay, Ann. of Math.105, 225–264 (1977)

    Article  MathSciNet  Google Scholar 

  38. Skoda, H.: Applications des techniquesL 2 à la théorie des ideaux d’un algèbre de fonctions holomorphes avec poids, Ann. Sci. Ecole Norm. Sup. ser.5 IV, 545–580 (1972)

    MATH  MathSciNet  Google Scholar 

  39. Takegoshi, K.: Torsion freeness theorems for higher direct image sheaves of semi-positive vector bundles, preprint.

  40. Kohn, J.J.: Boundary behaviour of\(\bar \partial\) on weakly pseudoconvex manifolds of dimension two, J. Diff. Geom.6, 523–542 (1972)

    MATH  MathSciNet  Google Scholar 

  41. Bonneau, P., Diederich, K.: Integral solution operators for the Cauchy-Riemann equations on psuedoconvex domains, Math. Ann.286, 77–100 (1990)

    Article  MATH  MathSciNet  Google Scholar 

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Ohsawa, T. On the extension ofL 2 holomorphic functions III: negligible weights. Math Z 219, 215–225 (1995). https://doi.org/10.1007/BF02572360

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