The minimum principle from a Hamiltonian point of view

1997/12/28 by Peter Heinzner, Heinzner, Peter · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.dg-ga/9712019

openalex publication_date 1997/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a complex Lie group, G_R a real form of G and X a G_R-stable domain of holomorphy in a complex G-manifold. If there is a G_R-invariant strictly plurisubharmonic function on X which has certain exhaustion properties, then we show that the extended domain G.X is also a domain of holomorphy. As an application we give a proof of the extended future tube conjecture. This is the assertion that G.X is a domain of holomorphy in the case where X is the N-fold product of the tube domain in C⁴ over the positive light cone in R⁴ and G is the connected complex Lorentz group acting diagonally.

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• Hamiltonian Actions on Homogeneous Bounded Domains

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