Harmonic, Monogenic and Hypermonogenic Functions on Some Conformally Flat Manifolds in $R^n$ arising from Special Arithmetic Groups of the Vahlen Group

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dc.creatorKrausshar, R. S.
dc.creatorRyan, John
dc.creatorYuying, Qiao
dc.date2004-04-19
dc.date.accessioned2026-07-07T05:07:33Z
dc.date.available2026-07-07T05:07:33Z
dc.descriptionThis paper focuses on the development of harmonic and Clifford analysis techniques in the context of some conformally flat manifolds that arise from factoring out a simply-connected domain from $R^n$ by special arithmetic subgroups of the conformal group. Our discussion encompasses in particular the Hopf manifold $S^1 \times S^{n-1}$, conformally flat cylinders and tori and some conformally flat manifolds of genus $g \ge 2$, such as $k$-handled tori and polycylinders. This paper provides a continuation as well as an extension of our previous two papers \cite{KraRyan1,KraRyan2}. In particular, we introduce a Cauchy integral formula for hypermonogenic functions on cylinders, tori and on half of the Hopf manifold. These are solutions to the Dirac-Hodge equation with respect to the hyperbolic metric. We further develop generalizations of the Mittag-Leffler theorem and the Laurent expansion theorem for cylindrical and toroidal monogenic functions. The study of Hardy space decompositions on the Hopf manifold is also continued. Kerzman-Stein operators are introduced. Explicit formulas for the Szegö kernel, the Bergman kernel and the Poisson kernel of half the Hopf manifold are given.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/math/0404337
dc.identifierhttp://arxiv.org/abs/math/0404337
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70897
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject53 C 27, 30 G 35, 42 B 35
dc.titleHarmonic, Monogenic and Hypermonogenic Functions on Some Conformally Flat Manifolds in $R^n$ arising from Special Arithmetic Groups of the Vahlen Group
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