Analytic functions, also known as holomorphic functions, form the cornerstone of complex analysis, widely studied for their elegant properties and deep connections in both pure and applied mathematics ...

Let R be a hyperbolic Riemann surface embedded in a compact Riemann surface of genus g and let f be an analytic function mapping R into R, f not the identity function. Then f has as most 2g + 2 ...

This is a preview. Log in through your library . Journal Information Annals of Mathematics, a distinguished journal of research papers in pure mathematics, was founded in 1884. Annals of Mathematics ...