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The first eigenvalue of the Laplacian on orientable surfaces
The famous Yang-Yau inequality provides an upper bound for the first eigenvalue of the Laplacian on an orientable Riemannian surface solely in terms of its genus $γ$ and the area. Its proof relies on the existence of holomorhic maps to $\mathbb{CP}^1$ of low degree. Very recently, A.~Ros was able to
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