A note on the regularity of the degenerate complex Monge-Ampère equation
Szymon Pliś (2010)
Annales Polonici Mathematici
Similarity:
We prove the almost regularity of the degenerate complex Monge-Ampère equation in a special case.
Szymon Pliś (2010)
Annales Polonici Mathematici
Similarity:
We prove the almost regularity of the degenerate complex Monge-Ampère equation in a special case.
Le Mau Hai, Nguyen Xuan Hong (2014)
Annales Polonici Mathematici
Similarity:
The aim of the paper is to investigate subextensions with boundary values of certain plurisubharmonic functions without changing the Monge-Ampère measures. From the results obtained, we deduce that if a given sequence is convergent in -capacity then the sequence of the Monge-Ampère measures of subextensions is weakly*-convergent. As an application, we investigate the Dirichlet problem for a nonnegative measure μ in the class ℱ(Ω,g) without the assumption that μ vanishes on all pluripolar...
Sławomir Kołodziej (2003)
Annales Polonici Mathematici
Similarity:
regularity of the solutions of the complex Monge-Ampère equation in ℂPⁿ with the n-root of the right hand side in is proved.
Rafał Czyż (2010)
Annales Polonici Mathematici
Similarity:
Let Ω be a bounded hyperconvex domain in ℂn and let μ be a positive and finite measure which vanishes on all pluripolar subsets of Ω. We prove that for every continuous and strictly increasing function χ:(-∞,0) → (-∞,0) there exists a negative plurisubharmonic function u which solves the Monge-Ampère type equation . Under some additional assumption the solution u is uniquely determined.
Azimbay Sadullaev (2012)
Annales Polonici Mathematici
Similarity:
We consider a class of maximal plurisubharmonic functions and prove several properties of it. We also give a condition of maximality for unbounded plurisubharmonic functions in terms of the Monge-Ampère operator .
Rafał Czyż (2001)
Annales Polonici Mathematici
Similarity:
We prove some existence results for the complex Monge-Ampère equation in ℂⁿ in a certain class of homogeneous functions in ℂⁿ, i.e. we show that for some nonnegative complex homogeneous functions g there exists a plurisubharmonic complex homogeneous solution u of the complex Monge-Ampère equation.
S. Hronek, R. Suchánek (2022)
Archivum Mathematicum
Similarity:
We study properties of pseudo-Riemannian metrics corresponding to Monge-Ampère structures on four dimensional . We describe a family of Ricci flat solutions, which are parametrized by six coefficients satisfying the Plücker embedding equation. We also focus on pullbacks of the pseudo-metrics on two dimensional , and describe the corresponding Hessian structures.
Kantorovich, L.V. (2004)
Journal of Mathematical Sciences (New York)
Similarity:
Mohamad Charabati (2015)
Annales Polonici Mathematici
Similarity:
We consider the Dirichlet problem for the complex Monge-Ampère equation in a bounded strongly hyperconvex Lipschitz domain in ℂⁿ. We first give a sharp estimate on the modulus of continuity of the solution when the boundary data is continuous and the right hand side has a continuous density. Then we consider the case when the boundary value function is and the right hand side has a density in for some p > 1, and prove the Hölder continuity of the solution.
Rafał Czyż, Lisa Hed (2008)
Annales Polonici Mathematici
Similarity:
We prove that subextension of certain plurisubharmonic functions is always possible without increasing the total Monge-Ampère mass.
Machida, Y., Morimoto, T. (1999)
Lobachevskii Journal of Mathematics
Similarity:
Pham Hoang Hiep (2005)
Annales Polonici Mathematici
Similarity:
We give a characterization for boundedness of plurisubharmonic functions in the Cegrell class ℱ.
Rafał Czyż, Per Åhag (2004)
Annales Polonici Mathematici
Similarity:
Let μ be a non-negative measure with finite mass given by , where ψ is a bounded plurisubharmonic function with zero boundary values and , φ ≥ 0, 1 ≤ q ≤ ∞. The Dirichlet problem for the complex Monge-Ampère operator with the measure μ is studied.
Jonas Wiklund (2004)
Annales Polonici Mathematici
Similarity:
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.
Szymon Pliś (2005)
Annales Polonici Mathematici
Similarity:
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.
Thierry Champion, Luigi De Pascale (2010)
Journal of the European Mathematical Society
Similarity:
We prove the existence of an optimal transport map for the Monge problem in a convex bounded subset of under the assumptions that the first marginal is absolutely continuous with respect to the Lebesgue measure and that the cost is given by a strictly convex norm. We propose a new approach which does not use disintegration of measures.
Rafał Czyż
Similarity:
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.
Nguyen Quang Dieu (2011)
Annales Polonici Mathematici
Similarity:
We give sufficient conditions for unicity of plurisubharmonic functions in Cegrell classes.
Laszló Lempert (1983)
Mathematische Annalen
Similarity:
Jan Chrastina (1989)
Časopis pro pěstování matematiky
Similarity:
Slimane Benelkourchi (2014)
Annales Polonici Mathematici
Similarity:
We show a very general existence theorem for a complex Monge-Ampère type equation on hyperconvex domains.
Matthew J. Gursky (2008)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Similarity:
We consider the Monge-Ampère-type equation , where is the Schouten tensor of a conformally related metric and is a suitably chosen constant. When the scalar curvature is non-positive we give necessary and sufficient conditions for the existence of solutions. When the scalar curvature is positive and the first Betti number of the manifold is non-zero we also establish existence. Moreover, by adapting a construction of Schoen, we show that solutions are in general not unique. ...
Sławomir Kołodziej (1996)
Annales Polonici Mathematici
Similarity:
We find a bounded solution of the non-homogeneous Monge-Ampère equation under very weak assumptions on its right hand side.