Cells of harmonicity

Kolář, Martin

  • Proceedings of the Winter School "Geometry and Physics", Publisher: Circolo Matematico di Palermo(Palermo), page [189]-196

Abstract

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[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.

How to cite

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Kolář, Martin. "Cells of harmonicity." Proceedings of the Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1991. [189]-196. <http://eudml.org/doc/221130>.

@inProceedings{Kolář1991,
abstract = {[For the entire collection see Zbl 0742.00067.]We are interested in partial differential equations on domains in $\mathcal \{C\}^n$. 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.},
author = {Kolář, Martin},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
keywords = {Srni (Czechoslovakia); Proceedings; Winter school; Geometry; Physics},
location = {Palermo},
pages = {[189]-196},
publisher = {Circolo Matematico di Palermo},
title = {Cells of harmonicity},
url = {http://eudml.org/doc/221130},
year = {1991},
}

TY - CLSWK
AU - Kolář, Martin
TI - Cells of harmonicity
T2 - Proceedings of the Winter School "Geometry and Physics"
PY - 1991
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [189]
EP - 196
AB - [For the entire collection see Zbl 0742.00067.]We are interested in partial differential equations on domains in $\mathcal {C}^n$. 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.
KW - Srni (Czechoslovakia); Proceedings; Winter school; Geometry; Physics
UR - http://eudml.org/doc/221130
ER -

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