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    Electronic Resource
    Electronic Resource
    Polynomial growth harmonic functions on connected sums of complete Riemannian manifolds (2000)
    Springer
    Mathematische Zeitschrift 233 (2000), S. 103-113 
    Details
    ISSN: 0025-5874
    Keywords: Mathematics Subject Classification (1991):31C05, 53C21, 58G03
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. Let M be a connected sum of complete Riemannian manifolds satisfying the volume doubling condition and the Poincaré inequality. We prove that the space of polynomial growth harmonic functions on M is finite dimensional whenever M has finitely many ends and satisfies the finite covering condition on each end. This result directly generalizes that of Tam, and it also partially generalizes that of Colding and Minicozzi II.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00004785
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