Geodesic
The minimum principle from a Hamiltonian point of view
Documenta mathematica, Tome 3 (1998), pp. 1-14.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $G$ be a complex Lie group and $G_\R$ a real form of $G$. For a $G_\R$-stable domain of holomorphy $X$ in a complex $G$-manifold we consider the question under which conditions the extended domain $G\cdot X$ is a domain of holomorphy. We give an answer in term of $G_\R$-invariant strictly plurisubharmonic functions on $X$ and the associate Marsden-Weinstein reduced space which is given by the Kaehler form and the moment map associated with the given strictly plurisubharmonic function. Our main application is a proof of the so called extended future tube conjecture which asserts that $G\cdot X$ is a domain of holomorphy in the case where $X$ is the $N$-fold product of the tube domain in $\C^4$ over the positive light cone and $G$ is the connected complex Lorentz group acting diagonally.
Classification : 32M05 
@article{DOCMA_1998__3__a15,
     author = {Heinzner, Peter},
     title = {The minimum principle from a {Hamiltonian} point of view},
     journal = {Documenta mathematica},
     pages = {1--14},
     publisher = {mathdoc},
     volume = {3},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_1998__3__a15/}
}
TY  - JOUR
AU  - Heinzner, Peter
TI  - The minimum principle from a Hamiltonian point of view
JO  - Documenta mathematica
PY  - 1998
SP  - 1
EP  - 14
VL  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_1998__3__a15/
LA  - en
ID  - DOCMA_1998__3__a15
ER  - 
%0 Journal Article
%A Heinzner, Peter
%T The minimum principle from a Hamiltonian point of view
%J Documenta mathematica
%D 1998
%P 1-14
%V 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_1998__3__a15/
%G en
%F DOCMA_1998__3__a15
Heinzner, Peter. The minimum principle from a Hamiltonian point of view. Documenta mathematica, Tome 3 (1998), pp. 1-14. http://geodesic.mathdoc.fr/item/DOCMA_1998__3__a15/