The Bers-Nielsen kernels and souls of open surfaces with negatice curvature
This paper establishes the following fine result: Theorem A: Let \(X\) be a Riemann surface of finite type \((n,k,m)\) with \(m\geq 1\) and \(2n-2+ k+m>0\). \([(n=\text{genus}\), \(m=\text{free-sides}\), \(k=\text{cups})]\), then the infinite Nielsen kernel \(N^ \infty(X)\) of \(X\) has no interior points. The infinite Nielsen kernel was defined by Bers by taking the (first) Nielsen kernel \((N(X))\) of \(X\) (replace free-sides by boundary geodesics) creating a new Riemann surface with boundary. Now let the boundary geodesics approach free-sides, giving a surface of the original type. Take the Nielsen kernel of this \(N^ 2(X)\). Continue in this way and define \(N^ \infty(X)= \bigcap_{k\geq 1} N^ k(X)\). The paper has a good bibliography of previous results concerning \(N^ \infty(X)\).
scientific article; zbMATH DE number 575617