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Search: MSC category 31C12 ( Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14] )

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1. CJM 2011 (vol 63 pp. 721)

Autin, Aymeric
Isoresonant Complex-valued Potentials and Symmetries
Let $X$ be a connected Riemannian manifold such that the resolvent of the free Laplacian $(\Delta-z)^{-1}$, $z\in\mathbb{C} \setminus \mathbb{R}^+$, has a meromorphic continuation through $\mathbb{R}^+$. The poles of this continuation are called resonances. When $X$ has some symmetries, we construct complex-valued potentials, $V$, such that the resolvent of $\Delta+V$, which has also a meromorphic continuation, has the same resonances with multiplicities as the free Laplacian.

Categories:31C12, 58J50

2. CJM 1998 (vol 50 pp. 547)

Gauthier, Paul M.
Mittag-Leffler theorems on Riemann surfaces and Riemannian manifolds
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
Categories:30F99, 31C12

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