Jump to ContentJump to Main Navigation
Advances in AnalysisThe Legacy of Elias M. Stein$
Users without a subscription are not able to see the full content.

Charles Fefferman, Alexandru D. Ionescu, D.H. Phong, and Stephen Wainger

Print publication date: 2014

Print ISBN-13: 9780691159416

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159416.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 23 July 2021

On the Singularities of the Pluricomplex Green’s Function

On the Singularities of the Pluricomplex Green’s Function

(p.419) Chapter Sixteen On the Singularities of the Pluricomplex Green’s Function
Advances in Analysis

D. H. Phong

Jacob Sturm

, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger
Princeton University Press

This chapter seeks to establish the existence of pluricomplex Green's functions with singularities at certain multi poles, given by arbitrary local analytic functions. The Green's function plays a central role in the study of functions of one complex variable or of two real variables. This chapter also attempts to develop a geometric/analytic approach to Monge-Ampère equations with measures on the right-hand side, where the singularities of the solution arise from blow-up constructions. Since blow-ups typically lead to degenerate Kähler forms, an essential tool in this chapter's approach is the recent existence theorems for the Dirichlet problem for complex Monge-Ampère equations with degenerate background form.

Keywords:   pluricomplex Green's functions, geometric approach, Monge-Ampère equations, singularities, blow-ups, Kähler forms

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.