Codazzi tensors and equations of Monge-Ampère type on compact manifolds of constant sectional curvature.

V.I. Oliker; U. Simon

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Displaying similar documents to “Codazzi tensors and equations of Monge-Ampère type on compact manifolds of constant sectional curvature.”

A C2-estimate for solutions of complex Monge-Ampère equations.

Friedmar Schulz (1984)

Journal für die reine und angewandte Mathematik

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On the second boundary value problem for equations of Monge-Ampère type.

John Urbas (1997)

Journal für die reine und angewandte Mathematik

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On a problem of Monge.

Kantorovich, L.V. (2004)

Journal of Mathematical Sciences (New York)

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Subextension of plurisubharmonic functions without increasing the total Monge-Ampère mass

Rafał Czyż, Lisa Hed (2008)

Annales Polonici Mathematici

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We prove that subextension of certain plurisubharmonic functions is always possible without increasing the total Monge-Ampère mass.

On decomposable Monge-Ampère equations.

Machida, Y., Morimoto, T. (1999)

Lobachevskii Journal of Mathematics

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Comparison Principles for Subelliptic Equations of Monge-Ampère Type

Martino Bardi, Paola Mannucci (2008)

Bollettino dell'Unione Matematica Italiana

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We present two comparison principles for viscosity sub- and supersolutions of Monge-Ampére-type equations associated to a family of vector fields. In particular, we obtain the uniqueness of a viscosity solution to the Dirichlet problem for the equation of prescribed horizontal Gauss curvature in a Carnot group.

Matrix inequalities and the complex Monge-Ampère operator

Jonas Wiklund (2004)

Annales Polonici Mathematici

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We study two known theorems regarding Hermitian matrices: Bellman's principle and Hadamard's theorem. Then we apply them to problems for the complex Monge-Ampère operator. We use Bellman's principle and the theory for plurisubharmonic functions of finite energy to prove a version of subadditivity for the complex Monge-Ampère operator. Then we show how Hadamard's theorem can be extended to polyradial plurisubharmonic functions.

A characterization of bounded plurisubharmonic functions

Pham Hoang Hiep (2005)

Annales Polonici Mathematici

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We give a characterization for boundedness of plurisubharmonic functions in the Cegrell class ℱ.

A counterexample to the regularity of the degenerate complex Monge-Ampère equation

Szymon Pliś (2005)

Annales Polonici Mathematici

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We modify an example due to X.-J. Wang and obtain some counterexamples to the regularity of the degenerate complex Monge-Ampère equation on a ball in ℂⁿ and on the projective space ℙⁿ.

The complex Monge-Ampère operator in the Cegrell classes

Rafał Czyż

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The complex Monge-Ampère operator is a useful tool not only within pluripotential theory, but also in algebraic geometry, dynamical systems and Kähler geometry. In this self-contained survey we present a unified theory of Cegrell's framework for the complex Monge-Ampère operator.