On the existence of Green’s function in Riemannian manifolds
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- by José L. Fernández PDF
- Proc. Amer. Math. Soc. 96 (1986), 284-286 Request permission
Abstract:
This note provides a sufficient condition of geometric character for the existence of Green’s function in an arbitrary complete Riemannian manifold.References
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L. V. Ahlfors, Sur le type d’une surface de Riemann, C. R. Acad. Sci. Paris 201 (1935), 30-32.
- Jozef Dodziuk, Every covering of a compact Riemann surface of genus greater than one carries a nontrivial $L^{2}$ harmonic differential, Acta Math. 152 (1984), no. 1-2, 49–56. MR 736211, DOI 10.1007/BF02392190
- Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
- R. E. Greene and H. Wu, Function theory on manifolds which possess a pole, Lecture Notes in Mathematics, vol. 699, Springer, Berlin, 1979. MR 521983, DOI 10.1007/BFb0063413
- John Milnor, On deciding whether a surface is parabolic or hyperbolic, Amer. Math. Monthly 84 (1977), no. 1, 43–46. MR 428232, DOI 10.2307/2318308 M. Tsuji, Potential theory in modern function theory, Chelsea, New York, 1973.
- Nicholas Th. Varopoulos, The Poisson kernel on positively curved manifolds, J. Functional Analysis 44 (1981), no. 3, 359–380. MR 643040, DOI 10.1016/0022-1236(81)90015-X
- N. T. Varopoulos, Potential theory and diffusion on Riemannian manifolds, Conference on harmonic analysis in honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981) Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, pp. 821–837. MR 730112
Additional Information
- © Copyright 1986 American Mathematical Society
- 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