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A Monge-Ampère inequality and applications to holomorphic mappings


Author: John P. D’Angelo
Journal: Proc. Amer. Math. Soc. 143 (2015), 4347-4359
MSC (2010): Primary 32W20, 32H35, 32U05
Published electronically: March 25, 2015
MathSciNet review: 3373933
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Abstract: We provide sufficient conditions for a variational inequality involving the complex Monge-Ampère determinant and give applications to proper holomorphic mappings. We also clarify the proof of a sharp inequality about volumes of holomorphic images by placing it in this more general context.


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Additional Information

John P. D’Angelo
Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 61801
Email: jpda@math.uiuc.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12557-9
Keywords: Proper holomorphic mappings, complex Monge-Amp\`ere determinant, volumes of holomorphic images, plurisubharmonic functions
Received by editor(s): January 27, 2014
Received by editor(s) in revised form: June 4, 2014
Published electronically: March 25, 2015
Additional Notes: The author acknowledges support from NSF Grant DMS 10-66177
Communicated by: Franc Forstneric
Article copyright: © Copyright 2015 American Mathematical Society