We discuss universal properties of general Teichmüller spaces. Our topics include the Teichmüller metric and the Kobayashi metric, extremality and unique extremality of quasiconformal mappings, biholomorphic maps between Teichmüller space, earthquakes and Thurston boundary.

Let Mn be a complete noncompact Kähler manifold with nonnegative bisectional curvature and maximal volume growth, we prove that M is biholomorphic to Cn. This confirms the uniformization conjecture of Yau when M has maximal volume growth.

A new proof of the assertion, that any global kähler deformation of a flag manifold F with b2 = 1 is biholomorphic to F , is given. Essential use is made of rational connectedness properties of F .

We show that if a holomorphic n-dimensional compact torus action on a compact connected complex manifold of complex dimension n has a fixed point then the manifold is equivariantly biholomorphic to a smooth toric variety.

We define the differential operator ∂ ∂z on infinitely differentiable functions (also called smooth or C∞ functions) on some open set in C by ∂ ∂z = 1 2 ( ∂ ∂x + i ∂ ∂y ). A quick calculation shows that ∂ ∂z obeys the product rule. Recall that a function f is holomorphic if and only if ∂ ∂z (f) = 0. A function is biholomorphic, or an analytic isomorphism, if it is holomorphic and has holomorphi...

0. Introduction Our object is to study domains which are the region of negative definiteness of an operator-valued Hermitian form defined on a space of operators and to investigate the biholomorphic linear fractional transformations between them. This is a unified setting in which to consider operator balls, operator half-planes, strictly J-contractive operators, strictly J-dissipative operator...