  The goal of this note is to introduce an interesting question proposed by D.
Rydh on an analytic version of the local structure of Artin stacks saying that
near points with linearly reductive stabilizers, Artin stacks are
\'etale-locally quotient stacks. We give some supporting evidence by verifying
it on two fundamental classes of classical analytic moduli spaces: the
Teichm\"uller moduli space and the Riemann moduli space of integrable complex
structures whose analytic stack versions have been constructed by a recent work
of L. Meersseman.

Algebraic Geometry;Complex Variables