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Value distribution theory for meromorphic maps [Libro electrónico] / autor: Wilhelm Stoll

Por: Stoll, Wilhelm [autor/a].
Tipo de material: Libro en línea Libro en línea Series Editor: Braunschweig, Baja Sajonia, Germany: Vieweg-Teubner Verlag, c1985Descripción: xi, 347 páginas ; 23 centímetros.ISBN: 3528089067; 9783663052944 (Print); 9783663052920 (Online).Tema(s): Value distribution theory | Nevanlinna theory | Functions, Meromorphic | Mappings (Mathematics)Nota de acceso: Disponible para usuarios de ECOSUR con su clave de acceso Nota de bibliografía: Incluye bibliografía e índice: páginas 334-343 Número de sistema: 56604Contenidos:Mostrar Resumen:
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Value distribution theory studies the behavior of mermorphic maps. Let f: M - N be a merom orphic map between complex manifolds. A target family CI ~ (Ea1aEA of analytic subsets Ea of N is given where A is a connected. compact complex manifold. The behavior of the inverse 1 family ["'(CI) = (f- {E )laEA is investigated. A substantial theory has been a created by many contributors. Usually the targets Ea stay fixed. However we can consider a finite set IJ of meromorphic maps g : M - A and study the incidence f{z) E Eg(z) for z E M and some g E IJ. Here we investigate this situation: M is a parabolic manifold of dimension m and N = lP n is the n-dimensional projective space. The family of hyperplanes in lP n is the target family parameterized by the dual projective space lP* We obtain a Nevanlinna theory consisting of several n First Main Theorems. Second Main Theorems and Defect Relations and extend recent work by B. Shiffman and by S. Mori. We use the Ahlfors-Weyl theory modified by the curvature method of Cowen and Griffiths. The Introduction consists of two parts. In Part A. we sketch the theory for fixed targets to provide background for those who are familar with complex analysis but are not acquainted with value distribution theory.

Recurso en línea: http://link.springer.com/openurl?genre=book&isbn=978-3-663-05294-4
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Incluye bibliografía e índice: páginas 334-343

1. Introdution.. 2. Hermitian geometry.. 3. Meromorphic maps on parabolic manifolds.. 4. The first main theorem.. 5. Associated maps.. 6. Frenet frames.. 7. The ahlfors estimates.. 8. General position.. 9. The second main theroem.. 10. Value distribution over a function field.. 11. An example.. 12. The theorem of nevanlinna-mori.. 13. References.. Index

Disponible para usuarios de ECOSUR con su clave de acceso

Value distribution theory studies the behavior of mermorphic maps. Let f: M - N be a merom orphic map between complex manifolds. A target family CI ~ (Ea1aEA of analytic subsets Ea of N is given where A is a connected. compact complex manifold. The behavior of the inverse 1 family ["'(CI) = (f- {E )laEA is investigated. A substantial theory has been a created by many contributors. Usually the targets Ea stay fixed. However we can consider a finite set IJ of meromorphic maps g : M - A and study the incidence f{z) E Eg(z) for z E M and some g E IJ. Here we investigate this situation: M is a parabolic manifold of dimension m and N = lP n is the n-dimensional projective space. The family of hyperplanes in lP n is the target family parameterized by the dual projective space lP* We obtain a Nevanlinna theory consisting of several n First Main Theorems. Second Main Theorems and Defect Relations and extend recent work by B. Shiffman and by S. Mori. We use the Ahlfors-Weyl theory modified by the curvature method of Cowen and Griffiths. The Introduction consists of two parts. In Part A. we sketch the theory for fixed targets to provide background for those who are familar with complex analysis but are not acquainted with value distribution theory. eng

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