References
[ABR]D. Arapura, P. Bressler, M. Ramachandran, On the fundamental group of a compact Kähler manifold, Duke Math. J. 64 (1992), 477–488.
[Au]T. Aubin, Nonlinear Analysis on Manifolds, Monge Ampère Equations (Grund. der math. Wiss. 252), Springer, Berlin-Heidelberg-New York, 1982.
[C]H. Cartan, Quotients of complex analytic spaces, in “Contributions to Function Theory”, International Colloquium on Function Theory 1960, 1–15, Tata Inst. of Fund. Res., Bombay 1960
[ChY]S.Y. Cheng, S.T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), 333–354.
[Cor]K. Corlette, FlatG-bundles with canonical metrics, J. Diff. Geom. 28 (1988), 361–382.
[Cou]P. Cousin, Sur les fonctions triplement périodiques de deux variables, Acta Math. 33 (1910), 105–232.
[D1]J.-P. Demailly, EstimationsL 2 pour l'operateur\(\bar \partial \) d'un fibré vectoriel holomorphe semi- positif au-dessus d'une variété kählerienne complète, Ann. Scient. Éc. Norm. Sup. 15 (1982), 457–511.
[D2]J.-P. Demailly, Cohomology ofq-convex spaces in top degrees, Math. Z. 204 (1990), 283–295.
[DiO]K. Diederich, T. Ohsawa, A Levi problem on two-dimensional complex manifolds, Math. Ann. 261 (1982), 255–261.
[F1]K. Fritzsche,q-konvexe Restmengen in kompakten komplexen Mannigfaltigkeiten, Math. Ann. 221, 251–273 (1976)
[F2]K. Fritzsche, Pseudoconvexity properties of complements of analytic subvarieties, Math. Ann. 230 (1977), 107–122.
[G]M. Gaffney, A special Stokes theorem for Riemannian manifolds, Ann. Math. 60 (1954), 140–145.
[GiTr]D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations of Second Order (Grund. der Math. Wiss. 224), Springer, Berlin-Heidelberg-New York, 1983.
[Gr1]H. Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331–368.
[Gr2]H. Grauert, Bemerkenswerte pseudokonvexe Mannigfaltigkeiten, Math. Z. 81 (1963), 377–391.
[GreWu]R.E. Greene, H. Wu,C ∞ approximations of convex, subharmonic, and plurisubharmonic functions, Ann. Scient. Éc. Norm. Sup. 12 (1979), 47–84.
[Gro1]M. Gromov, Sur le groupe fondamental d'une variété kählerienne, C.R. Acad. Sci. Paris 308 (1989), 67–70.
[Gro2]M. Gromov, Kähler hyperbolicity andL 2-Hodge Theory, J. Diff. Geom. 33, 263–292 (1991).
[GroSc]M. Gromov, R. Schoen, Harmonic maps into singular spaces andp-adic superrigidity for lattices in groups of rank one, Publ. Math. I.H.E.S. 76 (1992), 165–246.
[Gu]R. Gunning, Introduction to Holomophic Functions of Several Variables, Vol. I, Wadsworth, Belmont 1990.
[H]A. Huckleberry, The Levi problem on pseudoconvex manifolds which are not strongly pseudoconvex, Math. Ann. 219 (1976), 127–137.
[L]P. Li, On the structure of complete Kähler manifolds with nonnegative curvature near infinity, Invent. Math. 99 (1990), 579–600.
[LT1]P. Li, L.-F. Tam, Positive harmonic functions on complete manifolds with non-negative curvature outside a compact set, Ann. Math. 125 (1987), 171–207.
[LT2]P. Li, L.-F. Tam, The heat equation and harmonic maps of complete manifolds, Invent. Math. 105 (1991), 1–46.
[LT3]P. Li, L.-F. Tam, Harmonic functions and the structure of complete manifolds, J. Diff. Geom. 35 (1992), 359–383.
[N1]M. Nakai, On Evans potential, Proc. Japan. Acad. 38 (1962), 624–629.
[N2]M. Nakai, Infinite boundary value problems for second order elliptic partial differential equations, J. Fac. Sci. Univ. Tokyo, Sect. I 17 (1970), 101–121.
[Na]S. Nakano, Vanishing theorems for weakly 1-complete manifolds II, Publ. R.I.M.S. Kyoto 10 (1974), 101–110.
[Nar]R. Narasimhan, The Levi problem for complex spaces II, Math. Ann. 146 (1962), 195–216.
[No]M. Nori, Zariski's conjecture and related problems, Ann. Scient. Éc. Norm. Sup. 16 (1983), 305–344.
[O1]T. Ohsawa, Weakly 1-complete manifold and Levi problem. Publ. R.I.M.S. Kyoto 17 (1981), 153–164.
[O2]T. Ohsawa, Completeness of noncompact analytic spaces, Publ. R.I.M.S. Kyoto 20 (1984), 683–692.
[Re]R. Remmert, Reduction of complex spaces, in “Seminars on Analytic Functions, Vol. I”, 190–205, I.A.S., Princeton, 1957.
[RoSa]B. Rodin, L. Sario, Principal Functions, Princeton: Van Nostrand 1968.
[S]L. Saloff-Coste, Uniformly elliptic operators on Riemannian manifolds, J. Diff. Geom. 36 (1992), 417–450.
[SaN]L. Sario, M. Nakai, Classification Theory of Riemann Surfaces (Grund. der Math Wiss., Bd. 164), Springer, Berlin-Heidelberg-New York, 1970.
[SaNos]L. Sario, K. Noshiro, Value Distribution Theory, Van Nostrand, Princeton, 1966.
[Sch1]M. Schneider, Über eine Vermutung von Hartshorne, Math. Ann. 201 (1973), 221–229.
[Sch2]M. Schneider, Lefschetzsätze und Hyperkonvexität, Invent. Math. 31 (1975), 183–192.
[ScoW]P. Scott, T. Wall, Topological methods in group theory, in “Homological Group Theory”, London Math. Soc. Lect. Note Series 36, 137–203, Cambridge University Press, Cambridge, 1979.
[Su]D. Sullivan, Growth of positive harmonic functions and Kleinian group limit sets of zero planar measure and Hausdorff dimension two, in “Geometry Symposium, Utrecht 1980” Lect. Notes in Math. 894, 127–144, Springer, Berlin-Heidelberg-New York 1981.
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The research of the first author is partially supported by a Reidler Foundation grant, and the research of the second author is partially supported by NSF grant no. DMS9305745.
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Napier, T., Ramachandran, M. Structure theorems for complete Kähler manifolds and applications to Lefschetz type theorems. Geometric and Functional Analysis 5, 809–851 (1995). https://doi.org/10.1007/BF01897052
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DOI: https://doi.org/10.1007/BF01897052