Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Integral representations and the complex Monge-Ampère equation in strictly convex domains


Author: Nancy K. Stanton
Journal: Proc. Amer. Math. Soc. 75 (1979), 276-278
MSC: Primary 32A25
DOI: https://doi.org/10.1090/S0002-9939-1979-0532150-2
MathSciNet review: 532150
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a relationship between Aizenberg's integral representation formula for holomorphic functions in a strictly convex domain and the complex Monge-Ampère equation.


References [Enhancements On Off] (What's this?)

  • [1] P. Ahern and R. Schneider, The boundary behavior of Henkin's kernel, Pacific J. Math. 66 (1976), 9-14. MR 0435449 (55:8409)
  • [2] L. A. Aizenberg, Integral representations of functions which are holomorphic in convex regions of $ {{\mathbf{C}}^n}$ space, Dokl. Akad. Nauk SSSR 151 (1963), 1247-1249; English, transl., Soviet Math. Dokl. 4 (1963), 1149-1152.
  • [3] C. L. Fefferman, Monge-Ampère equations, the Bergman kernel and geometry of pseudoconvex domains, Ann. of Math. 103 (1976), 395-416. MR 0407320 (53:11097a)
  • [4] F. Norguet, Introduction aux fonctions de plusieurs variables complexes: représentations intégrales, Fonctions de Plusieurs Variables Complexes, 1-97, Lecture Notes in Math., no. 409, Springer-Verlag, Berlin and New York, 1974. MR 0369729 (51:5961)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32A25

Retrieve articles in all journals with MSC: 32A25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0532150-2
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society