Dirichlet Problem of Quaternionic Monge-Ampère Equations

Abstract

In this paper, the author studies quaternionic Monge-Ampère equations and obtains the existence and uniqueness of the solutions to the Dirichlet problem for such equations without any restriction on domains. Our paper not only answers to the open problem proposed by Semyon Alesker in [3], but also extends relevant results in [7] to the quaternionic vector space.

17 pages. All comments are welcome! To appear in Israel Journal of Mathematics. arXiv admin note: text overlap with arXiv:math/0606756 by other authors

References in corpus (1)

• On a class of fully nonlinear elliptic equations on Hermitian manifolds

Cited by in corpus (3)

• On the Alesker-Verbitsky conjecture on hyperKähler manifolds
• Weak solutions to the quaternionic Monge-Ampère equation
• Subsolution theorem and the Dirichlet problem for the quaternionic Monge-Ampere equation