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# Mittag-Leffler theorems on Riemann surfaces and Riemannian manifolds

Published:1998-06-01
Printed: Jun 1998
• Paul M. Gauthier
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## Abstract

Cauchy and Poisson integrals over {\it unbounded\/} sets are employed to prove Mittag-Leffler type theorems with massive singularities as well as approximation theorems for holomorphic and harmonic functions.
 Keywords: holomorphic, harmonic, Mittag-Leffler, Runge
 MSC Classifications: 30F99 - None of the above, but in this section 31C12 - Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14]