[For the entire collection see Zbl 0742.00067.]We are interested in partial differential equations on domains in ${𝒞}^n$. One of the most natural questions is that of analytic continuation of solutions and domains of holomorphy. Our aim is to describe the domains of holomorphy for solutions of the complex Laplace and Dirac equations. We call them cells of harmonicity. We deduce their properties mostly by examining geometrical properties of the characteristic surface (which is the same for both equations), namely the complex null cone. Further we apply these results to the case of analytic continuation from the Euclidean region into Minkowski space. We get a simple proof of a result by Gindikin and Henkin in dimension 4 and its generalization to higher dimensions.

EUDML-ID : urn:eudml:doc:221130
Mots clés:

@article{701493,
     title = {Cells of harmonicity},
     booktitle = {Proceedings of the Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1991},
     pages = {[189]-196},
     mrnumber = {MR1151905},
     zbl = {0768.32011},
     url = {http://dml.mathdoc.fr/item/701493}
}

Kolář, Martin. Cells of harmonicity, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books,  (1991), pp. [189]-196. http://gdmltest.u-ga.fr/item/701493/