论文标题
双曲线表面上的大型steklov特征值
Large Steklov eigenvalues on hyperbolic surfaces
论文作者
论文摘要
在本文中，我们首先构造了具有连接的地球边界的双曲线表面序列，以使第一个归一化的steklov特征值$ \tildeσ_1$倾向于无穷大。然后，我们证明，作为$ g \ rightArrow \ infty $，\ Mathcal {m} _ {g，n}（l_g）$满足$ \tildeσ_1（σ）> c \ cdot \ cdot \ cdot \ | l_g | _1 $ c $ c $是$ c $的正常常数。这里$ \ Mathcal {m} _ {g，n}（l_g）$是$ g $ $ g $和$ n $ thengus $ g $的夸张表面的模量空间，长度为$ l_g =（l_g^1，\ cdots，cdots，l_g^n）$ weil-petersson $ _g $ l_g $ l_ $ l_ l y $ l \ |满足某些条件。
In this paper, we first construct a sequence of hyperbolic surfaces with connected geodesic boundary such that the first normalized Steklov eigenvalue $\tildeσ_1$ tends to infinity. We then prove that as $g\rightarrow \infty$, a generic $Σ\in \mathcal{M}_{g,n}(L_g)$ satisfies $\tildeσ_1(Σ)>C\cdot \|L_g\|_1$ where $C$ is a positive universal constant. Here $\mathcal{M}_{g,n}(L_g)$ is the moduli space of hyperbolic surfaces of genus $g$ and $n$ boundary components of length $L_g=(L_g^1,\cdots, L_g^n)$ endowed with the Weil-Petersson metric where $\|L_g\|_1\rightarrow\infty$ satisfies certain conditions.
