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Research seminar "Geometric and Harmonic Analysis": Michael Heins (Würzurg), D2.314

Titel: Spectral Theory of the invariant Laplacian on the hyperbolic Disk and the Riemann Sphere

Abstract: We discuss a unifying complex analytic framework for the eigenvalue theory of the Laplace operators of the hyperbolic disk and the Riemann sphere. The principal strategy is to pass to two complex coordinates to work with holomorphic objects instead of real-analytic ones. Our main theorem consists in an intrinsic classification of the Möbius invariant eigenspaces of the Laplacians.

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