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A classical result of Nitsche [21] about the behaviour of the solutions to the Liouville equation ∆u = 4 e 2u near isolated singularities is generalized to solutions of the Gaussian curvature equation ∆u = −κ(z) e 2u where κ is a negative Hölder continuous function. As an application a higher–order version of the Yau–Ahlfors–Schwarz lemma for complete(More)
We prove a generalization of the Schwarz–Carathéodory reflection principle for analytic maps f from the unit disk into arbitrary Riemann surfaces equipped with a complete real analytic conformal Riemannian metric λ(w) |dw|. This yields a necessary and sufficient condition for f to have an analytic continuation in terms of the pullback of the metric λ(w)(More)
We establish an extension of Liouville's classical representation theorem for solutions of the partial differential equation ∆u = 4 e 2u and combine this result with methods from nonlinear elliptic PDE to construct holomorphic maps with prescribed critical points and specified boundary behaviour. For instance, we show that for every Blaschke sequence {z j }(More)
  • O. Roth
  • 1986
The STSF method (Spatial Transformation of Sound Fields) is extremely versatile in the way that any acoustical parameter (pressure, velocity or intensity) can be estimated in the half space in from of the noise object. This allows simulation of attenuation of noise sources on the surface of the noise object, and the effect in the far field can be estimated.
The subject of this paper is Beurling's celebrated extension of the Riemann mapping theorem [5]. Our point of departure is the observation that the only known proof of the Beurling–Riemann mapping theorem contains a number of gaps which seem inherent in Beurling's geometric and approx-imative approach. We provide a complete proof of the Beurling–Riemann(More)