Solvability of the quaternionic Monge-Ampère equation on compact manifolds with a flat hyperKähler metric

DOI10.1016/j.aim.2013.03.021zbMath1280.53045arXiv1108.5910OpenAlexW2094631923MaRDI QIDQ390999

Semyon Alesker

Publication date: 9 January 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.5910

zbMATH Keywords

quaternionsMonge-Ampère equationsCalabi-type problem

Mathematics Subject Classification ID

Calabi-Yau theory (complex-analytic aspects) (32Q25) Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Monge-Ampère equations (35J96)

Related Items (15)

Viscosity solutions to quaternionic Monge-Ampère equations ⋮ Dirichlet problem of quaternionic Monge-Ampère equations ⋮ A remark on the quaternionic Monge-Ampère equation on foliated manifolds ⋮ Fully non-linear elliptic equations on compact manifolds with a flat hyperkähler metric ⋮ A parabolic approach to the Calabi-Yau problem in HKT geometry ⋮ The \(C^0\) estimate for the quaternionic Calabi conjecture ⋮ A \(C^0\) \textit{a priori} estimate for the quaternionic Monge-Ampère equation in almost hyperhermitian geometry ⋮ On the Alesker-Verbitsky conjecture on hyperKähler manifolds ⋮ Subsolution theorem and the Dirichlet problem for the quaternionic Monge-Ampère equation ⋮ A variational approach to the quaternionic Monge-Ampère equation ⋮ Unnamed Item ⋮ Quasicontinuity and maximality of quaternionic plurisubharmonic functions ⋮ Quaternionic Monge-Ampère operator for unbounded plurisubharmonic functions ⋮ The continuity and range of the quaternionic Monge-Ampère operator on quaternionic space ⋮ A uniform estimate for general quaternionic Calabi problem (with appendix by Daniel Barlet)

Cites Work

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• Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables.
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• Métriques riemanniennes et courbure
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