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

In this text, we prove that every quaternionic-contact structure can be embedded in a quaternionic manifold.

Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We review the only direct search for quaternionic quantum mechanics yet carried out and outline a recent proposal by the present authors to look for quaternionic e...

We prove that any asymptotically locally Euclidean scalar-flat Kähler 4-orbifold whose isometry group contains a 2-torus is isometric, up to an orbifold covering, to a quaternionic-complex quotient of a k-dimensional quaternionic vector space by a (k − 1)-torus. In order to do so, we first prove that any compact anti-self-dual 4-orbifold with positive Euler characteristic whose isometry group c...

BACKGROUND Vascular malformations and hemangiomas, which are endothelial lesions of childhood, may result in considerable morbidity because they can cause discomfort and functional impairment and have a negative affect on the patient's appearance. Although vascular malformations may initially appear very similar to hemangiomas, they have distinct clinical courses. Infantile hemangiomas progress...

We define an (equivariant) quaternionic analytic torsion for antiselfdual vector bundles on quaternionic Kähler manifolds, using ideas by Leung and Yi. We compute this torsion for vector bundles on quaternionic homogeneous spaces with respect to any isometry in the component of the identity, in terms of roots and Weyl groups. 2000 Mathematics Subject Classification: 53C25, 58J52, 53C26, 53C35

We show that, if a quaternionic k-dimensional vector bundle l' over the quaternionic projective space Hpn is stably extendible and its non-zero top Pontrjagin class is not zero mod 2, then l' is stably equivalent to the Whitney sum of k quaternionic line bundles provided k S; n.

Real Clifford algebras for arbitrary numbers of space and time dimensions as well their representations in terms spinors are reviewed discussed. The classified isomorphic matrix real, complex or quaternionic type. Spinors defined elements minimal quasi-minimal left ideals within the algebra pin spin groups. Two types Dirac adjoint introduced carefully. relationship between mathematical structur...

This paper explores further the computation of quaternionic numerical range a complex matrix. We prove modified version conjecture by So and Thompson. Specifically, we show that shape for matrix depends on two real values. establish under which conditions bild coincides with its when is convex.