A priori estimates for a generalized Monge-Ampere PDE on some compact Kaehler manifolds

We study a fully non-linear PDE involving a linear combination of symmetric polynomials of the Kaehler form on a Kaehler manifold. A [Image omitted.]a priori estimate is proven in general and a gradient estimate is proven in certain cases. Independently, we also provide a method-of-continuity proof...

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Published inComplex variables and elliptic equations Vol. 61; no. 8; pp. 1037 - 1051
Main Author Pingali, Vamsi P
Format Journal Article
LanguageEnglish
Published 02.08.2016
Subjects
Complex variables
Estimates
Manifolds
Mathematical analysis
Nonlinearity
Polynomials
Symmetry
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Summary:We study a fully non-linear PDE involving a linear combination of symmetric polynomials of the Kaehler form on a Kaehler manifold. A [Image omitted.]a priori estimate is proven in general and a gradient estimate is proven in certain cases. Independently, we also provide a method-of-continuity proof via a path of Kaehler metrics to recover the existence of solutions in some of the known cases. Known results are then applied to an analytic problem arising from Chern-Weil theory and to a special Lagrangian-type equation arising from mirror symmetry.
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ISSN:1747-6933
1747-6941
DOI:10.1080/17476933.2015.1133616