3 papers
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…
math.SP2017
On branched minimal immersions of surfaces by first eigenfunctions
Donato Cianci, Mikhail Karpukhin, Vladimir Medvedev
It was proved by Montiel and Ros that for each conformal structure on a compact surface there is at most one metric which admits a minimal immersion into some unit sphere by first…