1. CJM 2012 (vol 65 pp. 721)
 Adamus, Janusz; Randriambololona, Serge; Shafikov, Rasul

Tameness of Complex Dimension in a Real Analytic Set
Given a real analytic set $X$ in a complex manifold and a positive
integer $d$, denote by $\mathcal A^d$ the set of points $p$ in $X$ at which
there exists a germ of a complex analytic set of dimension $d$ contained in $X$.
It is proved that $\mathcal A^d$ is a closed semianalytic subset of $X$.
Keywords:complex dimension, finite type, semianalytic set, tameness Categories:32B10, 32B20, 32C07, 32C25, 32V15, 32V40, 14P15 

2. CJM 2008 (vol 60 pp. 33)
 Braun, Rüdiger W.; Meise, Reinhold; Taylor, B. A.

Higher Order Tangents to Analytic Varieties along Curves. II
Let~$V$ be an analytic variety in some open set in~$\C^n$. For a
real analytic curve~$\gamma$ with $ \gamma(0) = 0 $ and $ d \ge 1 $
define $ V_t = t^{d}(V  \gamma(t)) $. It was shown in a previous
paper that the currents of integration over~$V_t$ converge to a
limit current whose support $ T_{\gamma,d} V $ is an algebraic
variety as~$t$ tends to zero. Here, it is shown that the canonical
defining function of the limit current is the suitably normalized
limit of the canonical defining functions of the~$V_t$. As a
corollary, it is shown that $ T_{\gamma,d} V $ is either
inhomogeneous or coincides with $ T_{\gamma,\delta} V $ for
all~$\delta$ in some neighborhood of~$d$. As another application it
is shown that for surfaces only a finite number of curves lead to
limit varieties that are interesting for the investigation of
Phragm\'enLindel\"of conditions. Corresponding results for limit
varieties $ T_{\sigma,\delta} W $ of algebraic varieties W along
real analytic curves tending to infinity are derived by a
reduction to the local case.
Category:32C25 

3. CJM 2003 (vol 55 pp. 64)
 Braun, Rüdiger W.; Meise, Reinhold; Taylor, B. A.

Higher Order Tangents to Analytic Varieties along Curves
Let $V$ be an analytic variety in some open set in $\mathbb{C}^n$
which contains the origin and which is purely $k$dimensional. For a
curve $\gamma$ in $\mathbb{C}^n$, defined by a convergent Puiseux
series and satisfying $\gamma(0) = 0$, and $d \ge 1$, define $V_t :=
t^{d} \bigl( V\gamma(t) \bigr)$. Then the currents defined by $V_t$
converge to a limit current $T_{\gamma,d} [V]$ as $t$ tends to zero.
$T_{\gamma,d} [V]$ is either zero or its support is an algebraic
variety of pure dimension $k$ in $\mathbb{C}^n$. Properties of such
limit currents and examples are presented. These results will be
applied in a forthcoming paper to derive necessary conditions for
varieties satisfying the local Phragm\'enLindel\"of condition that
was used by H\"ormander to characterize the constant coefficient
partial differential operators which act surjectively on the space of
all real analytic functions on $\mathbb{R}^n$.
Category:32C25 
