We prove rigidity results for holomorphic proper maps from the complex unit ball to the Type IV bounded symmetric domain when the codimension is small. In addition, a classification result is ...established in the codimension one case.
Nous prouvons des résultats de rigidité pour les applications holomorphes propres de la boule unitaire complexe au domaine symétrique borné de type IV lorsque la codimension est petite. Nous prouvons aussi un résultat de classification dans le cas de codimension un.
We construct a complete proper holomorphic embedding from any strictly pseudoconvex domain with C2-boundary in Cn into the unit ball of CN, for N large enough, thereby answering a question of Alarcón ...and Forstnerič, 2013.
We derive the explicit formula for the normalized rational proper holomorphic maps of
R
a
t
(
H
n
,
H
3
n
-
2
)
. As a consequence, we prove that these maps are determined by their three jets.
In this paper we study proper holomorphic maps between bounded symmetric domains when the source domain is not irreducible. More precisely, we provide sufficient conditions for semi-product proper ...holomorphic maps to be product proper. As an application we characterize proper holomorphic maps between equidimensional bounded symmetric domains.
We prove that two proper holomorphic polynomial maps between bounded symmetric domains of classical type which preserve the origin are equivalent if and only if they are isotropically equivalent. ...Using this property we show that each member of a one-parameter family of maps from a 2015 paper by the author is inequivalent.
Let
w
be an unbounded radial weight on the complex plane. We study the following approximation problem: find a proper holomorphic map
f
:
C
→
C
n
such that |
f
| is equivalent to
w
. We give several ...characterizations of those
w
for which the problem is solvable. In particular, a constructive characterization is given in terms of tropical power series. Moreover, the following natural objects and properties are involved: essential weights on the complex plane, approximation by power series with positive coefficients, and approximation by the maximum of a holomorphic function modulus. Extensions to several complex variables and approximation by harmonic maps are also considered.
It is a classical problem in algebraic geometry to characterize the algebraic subvariety by using the Gauss map. In this note, we study the analogous phenomenon in CR geometry. In particular, under ...some assumptions, we show that a CR map between spheres is totally geodesic if and only if the CR Gauss map of the image is degenerate.
Under a potential-theoretical hypothesis named
f
-property which holds for all pseudoconvex domains of finite type and many examples of infinite type, we give a new method for constructing a family ...of bumping functions and hence plurisubharmonic peak functions with good estimates. The rate of lower bounds on the Kobayashi metric follows by the estimates of peak functions. The application to the continuous extendibility of proper holomorphic maps is given.
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