Daniela Kraus

The behaviour of solutions of the Gaussian curvature equation near an isolated boundary point

A classical result of Nitsche [22] about the behaviour of the solutions to the Liouville equation ?u = 4e2u near isolated singularities is generalized to solutions of the Gaussian curvature equation ?u = -?(z)e2u where ? is a negative Holder continuous function. As an application a higher-order version of the Yau-Ahlfors-Schwarz lemma for complete conformal Riemannian metrics is obtained.

Critical sets of bounded analytic functions, zero sets of Bergman spaces and nonpositive curvature

A classical result due to Blaschke states that for every analytic self-map

Critical points of inner functions, nonlinear partial differential equations, and an extension of Liouville's theorem

f

Critical Points, the Gauss Curvature Equation and Blaschke Products

of the open unit disk of the complex plane there exists a Blaschke product

On Beurling's boundary value problem in circle packing

B

On the isolated singularities of the solutions of the Gaussian curvature equation for nonnegative curvature

such that the zero sets of

Strong submultiplicativity of the Poincaré metric

f

A boundary version of Ahlfors’ Lemma, locally complete conformal metrics and conformally invariant reflection principles for analytic maps

and

Metrics with conical singularities on the sphere and sharp extensions of the theorems of Landau and Schottky

B

WEIGHTED DISTORTION IN CONFORMAL MAPPING IN EUCLIDEAN, HYPERBOLIC AND ELLIPTIC GEOMETRY

agree. In this paper we show that there is an analogue statement for critical sets, i.e. for every analytic self-map