On Some Holomorphic Cohomological Equations

Aziz El Kacimi Alaoui (1)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

Let Σ be a non compact Riemann surface and γ:Σ⟶Σ an automorphism acting freely and properly such that the quotient M = Σ/γ is a non compact Riemann surface. Using the fact that Σ and M are Stein manifolds, we prove that, for any holomorphic function g:Σ⟶C and any λ∈C , there exists a holomorphic function f:Σ⟶C which is a solution of the holomorphic cohomological equation f∘γ−λf=g

Mots clés: Cohomological equation; Holomorphic line bundle; Spectrum

Domaines: Mathématiques [math]

Aziz El Kacimi Alaoui. On Some Holomorphic Cohomological Equations. Results in mathematics = Resultate der Mathematik, 2013, 63 (1-2), pp.329-334. ⟨10.1007/s00025-011-0201-2⟩. ⟨hal-03148580⟩