Harmonic functions of polynomial growth on complete manifolds II
نویسندگان
چکیده
منابع مشابه
Harmonic Functions with Polynomial Growth
Twenty years ago Yau generalized the classical Liouville theo rem of complex analysis to open manifolds with nonnegative Ricci curva ture Speci cally he proved that a positive harmonic function on such a manifold must be constant This theorem of Yau was considerably generalized by Cheng Yau see by means of a gradient estimate which implies the Harnack inequality As a consequence of this gradien...
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Let M be a complete simply connected manifold which is in addition Gromov hyperbolic, coercive and roughly starlike. For a given harmonic function on M , a local Fatou Theorem and a pointwise criteria of nontangential convergence coming from the density of energy are shown: at almost all points of the boundary, the harmonic function converges non-tangentially if and only if the supremum of the ...
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We give conditions under which the space of bounded harmonic functions on a Riemannian manifold M is naturally isomorphic to the space of bounded harmonic functions of a Markov chain on a discrete net X M arising from a discretization procedure for the pair (M; X). If, further, M is a regular covering manifold and the net is invariant with respect to the deck transformation group, then the entr...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1995
ISSN: 0025-5645
DOI: 10.2969/jmsj/04710037