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On the existence of Green's function in Riemannian manifolds


Author: José L. Fernández
Journal: Proc. Amer. Math. Soc. 96 (1986), 284-286
MSC: Primary 31C12; Secondary 58G25
DOI: https://doi.org/10.1090/S0002-9939-1986-0818459-7
MathSciNet review: 818459
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Abstract: This note provides a sufficient condition of geometric character for the existence of Green's function in an arbitrary complete Riemannian manifold.


References [Enhancements On Off] (What's this?)

  • [A] L. V. Ahlfors, Sur le type d'une surface de Riemann, C. R. Acad. Sci. Paris 201 (1935), 30-32.
  • [D] J. Dodziuk, Every covering of a compact Riemannian surface of genus greater that one carries a nontrivial $ {L^2}$ harmonic differential, Acta Math. 152 (1984), 49-56. MR 736211 (85j:30090)
  • [F] H. Fédérer, Geometric measure theory, Springer-Verlag, New York, 1969. MR 0257325 (41:1976)
  • [GW] R. Greene and H. Wu, Function theory on manifolds which possess a pole, Lecture Notes in Math., vol. 699, Springer-Verlag, Berlin and New York, 1979. MR 521983 (81a:53002)
  • [M] J. Milnor, On deciding whether a surface is parabolic or hyperbolic, Amer. Math. Monthly 84 (1977), 43-46. MR 0428232 (55:1257)
  • [T] M. Tsuji, Potential theory in modern function theory, Chelsea, New York, 1973.
  • [V1] N. T. Varopoulos, The Poisson kernel on positively curved manifolds, J. Funct. Anal. 44 (1981), 109-118. MR 643040 (84h:58142a)
  • [V2] -, Potential theory and diffusion on Riemannian manifolds, Conference in Harmonic Analysis in Honor of Antoni Zygmund, Wadsworth, Belmont, Calif. 1983. MR 730112 (85a:58103)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0818459-7
Article copyright: © Copyright 1986 American Mathematical Society

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