Finite parts of the spectrum of a Riemann surface.

Peter Buser; Gilles Courtois

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The Hatcher-Waldhausen map is a spectrum map.

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Koebe's general uniformisation theorem for planar Riemann surfaces

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We give a complete and transparent proof of Koebe's General Uniformisation Theorem that every planar Riemann surface is biholomorphic to a domain in the Riemann sphere ℂ̂, by showing that a domain with analytic boundary and at least two boundary components on a planar Riemann surface is biholomorphic to a circular-slit annulus in ℂ.