A Theorem on the Extension of a Holomorphic Function Defined on an Algebraic Variety to an Entire Function
This paper investigates the properties of the order and type of holomorphic functions
defined on a regular compact set K of an algebraic variety A. Furthermore, we prove a theorem on
the holomorphic extension of a function defined on K to an entire function on the whole algebraic
variety A.
1. A. Zeriahi, Approximation polynomiale et extension holomorphe avec croissance sur une vari´ et´ e alg´ ebrique.
Ann. Polon. Math. 63 (1996), 35-50
2. P. Griffiths and J. King, Nevanlinna Theory and Holomorphic Mappings Between Algebraic Varieties,
Acta Mathematica, 130 (1973), 145–220.
3. A. Aytuna and A. Sadullaev, Polynomials on Parabolic Manifolds, Contemporary Mathematics.
4. A. Aytuna and A. Sadullaev, Polynomials on Parabolic Manifolds, Contemporary Mathematics, No. 662,
2016, pp. 1–22.
5. E. Bedford and B. A. Taylor, A New Capacity for Plurisubharmonic Functions, Acta Mathematica,
Vol. 149, 1982, pp. 1–40.
6. B. Berndtsson and M. PIaun, Quantitative Extensions of Pluricanonical Forms and Closed Positive
Currents, Nagoya Mathematical Journal, Vol. 205, 2012, pp. 25–65.
7. D. Coman, V. Guedj and A. Zeriahi, Extension of Plurisubharmonic Functions with Growth Control,
Journal für die Reine und Angewandte Mathematik, Vol. 676, 2013, pp. 33–49.
8. T. Darvas, E. Di Nezza and C. H. Lu, Monotonicity of Nonpluripolar Products and Complex Monge–
Amp` ere Equations with Prescribed Singularity, Analysis & PDE, Vol. 11, No. 8, 2018, pp. 2049–2087.
9. J. P. Demailly, Mesures de Monge–Amp` ere et Caract´ erisation G´ eom´ etrique des Vari´ et´ es Alg´ ebriques
Affines, M´ emoires de la Soci´ et´ e Math´ ematique de France, No. 19, 1985, pp. 1–128.
10. J. P. Demailly, Complex Analytic and Differential Geometry, Available online:
11. P. Griffiths and J. King, Nevanlinna Theory and Holomorphic Mappings Between Algebraic Varieties,
Acta Mathematica, Vol. 130, 1973, pp. 145–220.
12. A. Sadullaev, Plurisubharmonic Measures and Capacities on Complex Manifolds, Russian Mathematical
Surveys, Vol. 36, No. 4, 1981, pp. 53–105.
13. A. Sadullaev, Estimates of Polynomials on Analytic Sets, Izvestiya Akademii Nauk SSSR. Seriya Matem-
aticheskaya, Vol. 46, No. 3, 1982, pp. 524–534.
14. A. Sadullaev, Plurisubharmonic Functions, In: Itogi Nauki i Tekhniki. Sovremennye Problemy Matem-
atiki. Fundamental Directions, VINITI, Moscow, Vol. 8, 1985, pp. 65–113.
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