Displaying similar documents to “A viscosity approach to degenerate complex Monge-Ampère equations”

The complex Monge-Ampère operator in the Cegrell classes

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.

Convergence in capacity on smooth hypersurfaces of compact Kähler manifolds

Vu Viet Hung, Hoang Nhat Quy (2012)

Annales Polonici Mathematici

Similarity:

We study restrictions of ω-plurisubharmonic functions to a smooth hypersurface S in a compact Kähler manifold X. The result obtained and the characterization of convergence in capacity due to S. Dinew and P. H. Hiep [to appear in Ann. Scuola Norm. Sup. Pisa Cl. Sci.] are used to study convergence in capacity on S.

Toric extremal Kähler-Ricci solitons are Kähler-Einstein

Simone Calamai, David Petrecca (2017)

Complex Manifolds

Similarity:

In this short note, we prove that a Calabi extremal Kähler-Ricci soliton on a compact toric Kähler manifold is Einstein. This settles for the class of toric manifolds a general problem stated by the authors that they solved only under some curvature assumptions.

ω-pluripolar sets and subextension of ω-plurisubharmonic functions on compact Kähler manifolds

Le Mau Hai, Nguyen Van Khue, Pham Hoang Hiep (2007)

Annales Polonici Mathematici

Similarity:

We establish some results on ω-pluripolarity and complete ω-pluripolarity for sets in a compact Kähler manifold X with fundamental form ω. Moreover, we study subextension of ω-psh functions on a hyperconvex domain in X and prove a comparison principle for the class 𝓔(X,ω) recently introduced and investigated by Guedj-Zeriahi.

An extension theorem for Kähler currents with analytic singularities

Tristan C. Collins, Valentino Tosatti (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

We prove an extension theorem for Kähler currents with analytic singularities in a Kähler class on a complex submanifold of a compact Kähler manifold.

Kähler-Einstein metrics: Old and New

Daniele Angella, Cristiano Spotti (2017)

Complex Manifolds

Similarity:

We present classical and recent results on Kähler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of stability (K-stability). These are the notes for the SMI course "Kähler-Einstein metrics" given by C.S. in Cortona (Italy), May 2017. The material is not intended to be original.

Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields

Frédéric Campana, Henri Guenancia, Mihai Păun (2013)

Annales scientifiques de l'École Normale Supérieure

Similarity:

We prove the existence of non-positively curved Kähler-Einstein metrics with cone singularities along a given simple normal crossing divisor of a compact Kähler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved Kähler-Einstein metrics with cone singularities. As an application we extend to this setting classical results of Lichnerowicz and Kobayashi on the parallelism and vanishing of appropriate holomorphic tensor fields. ...

Matrix inequalities and the complex Monge-Ampère operator

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.

Hermitian curvature flow

Jeffrey Streets, Gang Tian (2011)

Journal of the European Mathematical Society

Similarity:

We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler–Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler–Einstein metrics, and are automatically Kähler–Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existence and regularity results for this flow, as well as stability for the flow near Kähler–Einstein...