Common boundary regular fixed points for holomorphic semigroups in strongly convex domains

2014/02/15 by Marco Abate, Filippo Bracci, Abate, Marco +1
Computer Science · Mathematics · #Advanced Banach Space Theory #Advanced Mathematical Modeling in Engineering #Holomorphic and Operator Theory #math.CV #math.DS

paper · pdf · doi:10.48550/arxiv.1402.3675

arxiv created 2014/02/15 · arxiv updated 2014/02/18

Abstract

Let D be a bounded strongly convex domain with smooth boundary in \mathbb C^N. Let (ϕ_t) be a continuous semigroup of holomorphic self-maps of D. We prove that if p∈ ∂ D is an isolated boundary regular fixed point for ϕ_t0 for some t₀>0, then p is a boundary regular fixed point for ϕ_t for all t≥ 0. Along the way we also study backward iteration sequences for elliptic holomorphic self-maps of D.

Related

• Pluripotential theory, semigroups and boundary behavior of infinitesimal generators in strongly convex domains
• Two boundary rigidity results for holomorphic maps
• Backward iteration in strongly convex domains
• Boundary behavior and rigidity of semigroups of holomorphic mappings
• Separation of Boundary Singularities for Holomorphic Generators