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# Isoresonant Complex-valued Potentials and Symmetries

Published:2011-05-25
Printed: Aug 2011
• Aymeric Autin,
11 rue Hélène Boucher, 85400 Luçon, France
 Format: LaTeX MathJax PDF

## Abstract

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.
 MSC Classifications: 31C12 - Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14] 58J50 - Spectral problems; spectral geometry; scattering theory [See also 35Pxx]

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