Let be the sheaf of holomorphic functions on the compact connected complex manifold X, then by the maximum principle, global sections are constant, ie.
In mathematics, Grunsky's theorem, due to the German mathematician Helmut Grunsky, is a result in complex analysis concerning holomorphic univalent functions defined on the unit disk in the complex numbers.
The word "holomorphic" was introduced by two of Cauchy's students, Briot (1817–1882) and Bouquet (1819–1895), and derives from the Greek ὅλος (holos) meaning "entire", and μορφή (morphē) meaning "form" or "appearance".
In mathematics, a Veech surface is a translation surface (X,ω) (a Riemann surface X with a holomorphic 1-form ω) whose group SL(X,ω) of affine diffeomorphisms is a lattice in SL2(R) (a discrete subgroup of cofinite volume).