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math.DG2026
Uniform spectral gaps for random hyperbolic surfaces with not many cusps
Yuxin He, Yunhui Wu, Yuhao Xue
In this paper, we investigate uniform spectral gaps for Weil-Petersson random hyperbolic surfaces with not many cusps. We show that if where $α\in \left[0,\frac{1}{2}\…
math.DG2025
Short geodesics and multiplicities of eigenvalues of hyperbolic surfaces
Xiang He, Yunhui Wu, Haohao Zhang
In this paper, we obtain upper bounds on the multiplicity of Laplacian eigenvalues for closed hyperbolic surfaces in terms of the number of short closed geodesics and the genus …
math.DG2025
Spectral gaps on thick part of moduli spaces
Yunhui Wu, Haohao Zhang
In this paper, we study spectral gaps of closed hyperbolic surfaces for large genus. We show that for any fixed , as the genus goes to infinity, the maximum of $λ_k-λ_{k…