Quaternionic Monge-Ampere equations

Abstract

The main result of this paper is the existence and uniqueness of solution of the Dirichlet problem for quaternionic Monge-Ampere equations in quaternionic strictly pseudoconvex bounded domains in H^n. We continue the study of the theory of plurisubharmonic functions of quaternionic variables started by the author at [2].

48 pages. The definition of quaternionic Hessian is replaced with the transposed matrix as it should be

References in corpus (1)

• Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables

Cited by in corpus (12)

• Quaternionic contact Einstein structures and the quaternionic contact Yamabe problem
• Valuations on convex sets, non-commutative determinants, and pluripotential theory
• On quaternionic Monge-Ampere operator, closed positive currents and Lelong-Jensen type formula on quaternionic space
• Potential theory in several quaternionic variables
• Dirichlet Problem of Quaternionic Monge-Ampère Equations
• Viscosity solutions to quaternionic Monge-Ampère equations
• On the Alesker-Verbitsky conjecture on hyperKähler manifolds
• Weak solutions to the quaternionic Monge-Ampère equation
• Quaternionic Monge-Ampere equation and Calabi problem for HKT-manifolds
• Subsolution theorem and the Dirichlet problem for the quaternionic Monge-Ampere equation
• Plurisubharmonic functions on the octonionic plane and Spin(9)-invariant valuations on convex sets
• Balanced HKT metrics and strong HKT metrics on hypercomplex manifolds