21 citations · 32 across the 3 of their papers we have counts for
7 papers · 1 filter
Semigroups versus evolution families in the Loewner theory
Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal
We show that an evolution family of the unit disc is commuting if and only if the associated Herglotz vector field has separated variables. This is the case if and only if the evol…
Loewner chains in the unit disk
Manuel D. Contreras, Santiago Diaz-Madrigal, Pavel Gumenyuk
In this paper we introduce a general version of the notion of Loewner chains which comes from the new and unified treatment, given in [arXiv:0807.1594], of the radial and chordal v…
Evolution Families and the Loewner Equation II: complex hyperbolic manifolds
Filippo Bracci, Manuel D. Contreras, S. Diaz-Madrigal
We prove that evolution families on complex complete hyperbolic manifolds are in one to one correspondence with certain semicomplete non-autonomous holomorphic vector fields, provi…
Evolution Families and the Loewner Equation I: The Unit Disc
Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal
In this paper we introduce a general version of the Loewner differential equation which allows us to present a new and unified treatment of both the radial equation introduced in 1…
Aleksandrov-Clark measures and semigroups of analytic functions in the unit disc
Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal
In this paper we prove a formula describing the infinitesimal generator of a continuous semigroup $(\v_t)$ of holomorphic self-maps of the unit disc with respect to a boundary regu…
Pluripotential theory, semigroups and boundary behavior of infinitesimal generators in strongly convex domains
Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal
We characterize infinitesimal generators of semigroups of holomorphic self-maps of strongly convex domains using the pluricomplex Green function and the pluricomplex Poisson kernel…