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A majorant problem.

Peretz, Ronen (1992)

International Journal of Mathematics and Mathematical Sciences

A maximum principle for the Bergman space.

Boris Korenblum (1991)

Publicacions Matemàtiques

Let f(z) and g(z) be holomorphic in the open unit disk D and let Zf and Zg be their zero sets. If Zf ⊃ Zg and |f(z)| ≥ |g(z)| (1/2 e-2 < |z| < 1), then || f || ≥ || g || where || · || is the Bergman norm: || f ||2 = π-1 ∫D |f(z)|2 dm (dm is the Lebesgue area measure).

A new characterization of Gromov hyperbolicity for negatively curved surfaces.

José M. Rodríguez, Eva Tourís (2006)

Publicacions Matemàtiques

In this paper we show that to check Gromov hyperbolicity of any surface of constant negative curvature, or Riemann surface, we only need to verify the Rips condition on a very small class of triangles, namely, those obtained by marking three points in a simple closed geodesic. This result is, in fact, a new characterization of Gromov hyperbolicity for Riemann surfaces.

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