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Moduli spaces of abelian differentials : the principal boundary, counting problems, and the Siegel-Veech constants

Alex Eskin, Howard Masur, Anton Zorich (2003)

Publications Mathématiques de l'IHÉS

A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment (saddle connection) joining a pair of conical points one can find with a nonzero probability another saddle connection on S having the same direction and the same length as the initial one. A similar phenomenon is valid for the families of parallel closed geodesics. We give a complete description of...

Monge-Ampère measures and Poletsky-Stessin Hardy spaces on bounded hyperconvex domains

Sibel Şahin (2015)

Banach Center Publications

Poletsky-Stessin Hardy (PS-Hardy) spaces are the natural generalizations of classical Hardy spaces of the unit disc to general bounded, hyperconvex domains. On a bounded hyperconvex domain Ω, the PS-Hardy space H u p ( Ω ) is generated by a continuous, negative, plurisubharmonic exhaustion function u of the domain. Poletsky and Stessin considered the general properties of these spaces and mainly concentrated on the spaces H u p ( Ω ) where the Monge-Ampère measure ( d d c u ) has compact support for the associated exhaustion...

Morera type problems in Clifford analysis.

Emilio Marmolejo Olea (2001)

Revista Matemática Iberoamericana

The Pompeiu and the Morera problems have been studied in many contexts and generality. For example in different spaces, with different groups, locally, without an invariant measure, etc. The variations obtained exhibit the fascination of these problems.In this paper we present a new aspect: we study the case in which the functions have values over a Clifford Algebra. We show that in this context it is completely natural to consider the Morera problem and its variations. Specifically, we show the...

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