Concepedia

Monge-Ampere equation on compact Kahler manifolds

Indiana University Mathematics Journal · 2003 · 109 citations · 5 references

Concepts

Natural SciencesEnologyModern PhilosophyComplex GeometryStability TheoryCompact Complex ManifoldsCompactness TheoremsComplex Differential GeometryComplex Monge-ampère EquationsKähler Geometry

Abstract

We prove a stability theorem for generalized solutions of the complex Monge-Ampere equation. The uniqueness and equicontinuity of families of solutions follow from it.

References

5

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Natural Sciences, Mathematics, Physics +3

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Luis Caffarelli, J. J. Kohn, Louis Nirenberg et al. · Communications on Pure and Applied Mathematics · 1985 · 325 citations

Natural Sciences, Mathematics, Differential Equations +11

A numerical criterion for very ample line bundles

Jean-Pierre Demailly · Journal of Differential Geometry · 1993 · 251 citations · Full text

Natural Sciences, Mathematics, Geometry +10

Embedding of open riemannian manifolds by harmonic functions

Robert E. Greene, H. Wu · Annales de l’institut Fourier · 1975 · 111 citations · Full text

Natural Sciences, Mathematics, Computational Geometry +9

On the dirichlet problem for the complex Monge-Amp�re operator

Urban Cegrell · Mathematische Zeitschrift · 1984 · 76 citations

Natural Sciences, Mathematics, Physics +11