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math.DG2021
The first eigenvalue of the Laplacian on orientable surfaces
Mikhail Karpukhin, Denis Vinokurov
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 and the area.…
math.DG2019
On the Yang-Yau inequality for the first Laplace eigenvalue
Mikhail Karpukhin
In a seminal paper published in 1980, P. C. Yang and S.-T. Yau proved an inequality bounding the first eigenvalue of the Laplacian on an orientable Riemannian surface in terms of i…