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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard


IMPACT FACTOR 2018: 0.789

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.329
Source Normalized Impact per Paper (SNIP) 2018: 0.908

Mathematical Citation Quotient (MCQ) 2018: 0.53

Online
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1615-7168
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Volume 8, Issue 4

Issues

Finite type Monge–Ampère foliations

Morris Kalka
  • Mathematics Department, Tulane University, 6823 St. Charles Ave., New Orleans, LA 70118, USA. Email:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Giorgio Patrizio
Published Online: 2008-11-28 | DOI: https://doi.org/10.1515/ADVGEOM.2008.031

Abstract

For plurisubharmonic solutions of the complex homogeneous Monge–Ampère equation whose level sets are hypersurfaces of finite type, in dimension 2, it is shown that the Monge–Ampère foliation is defined even at points of higher degeneracy. The result is applied to provide a positive answer to a question of Burns on homogeneous polynomials whose logarithms satisfy the complex Monge–Ampère equation and to generalize the work of P. M. Wong on the classification of complete weighted circular domains.

About the article

Received: 2006-11-24

Revised: 2008-03-03

Published Online: 2008-11-28

Published in Print: 2008-10-01


Citation Information: Advances in Geometry, Volume 8, Issue 4, Pages 491–502, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/ADVGEOM.2008.031.

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[1]
Morris Kalka and Giorgio Patrizio
Annali di Matematica Pura ed Applicata, 2010, Volume 189, Number 3, Page 381

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