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Finite type Monge–Ampère foliations
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Morris Kalka
Published/Copyright:
November 28, 2008
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.
Received: 2006-11-24
Revised: 2008-03-03
Published Online: 2008-11-28
Published in Print: 2008-October
© de Gruyter 2008
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Articles in the same Issue
- Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three
- Finite type Monge–Ampère foliations
- The horofunction boundary of the Hilbert geometry
- Counting the hyperplane sections with fixed invariants of a plane quintic – three approaches to a classical enumerative problem
- Totally non-real divisors in linear systems on smooth real curves
- Covers of Klein surfaces
- A classification of polarized manifolds by the sectional Betti number and the sectional Hodge number
- On reduced polytopes and antipodality
