1. CJM 2016 (vol 68 pp. 841)
 Gupta, Sanjiv Kumar; Hare, Kathryn

Characterizing the Absolute Continuity of the Convolution of Orbital Measures in a Classical Lie Algebra
Let $\mathfrak{g}$ be a compact, simple Lie algebra of dimension
$d$. It is
a classical result that the convolution of any $d$ nontrivial,
$G$invariant,
orbital measures is absolutely continuous with respect to
Lebesgue measure on $\mathfrak{g}$ and the sum of any $d$ nontrivial
orbits
has nonempty interior. The number $d$ was later reduced to the
rank of the
Lie algebra (or rank $+1$ in the case of type $A_{n}$). More
recently, the
minimal integer $k=k(X)$ such that the $k$fold convolution of
the orbital
measure supported on the orbit generated by $X$ is an absolutely
continuous
measure was calculated for each $X\in \mathfrak{g}$.
In this paper $\mathfrak{g}$ is any of the classical, compact,
simple Lie
algebras. We characterize the tuples $(X_{1},\dots,X_{L})$, with
$X_{i}\in
\mathfrak{g},$ which have the property that the convolution of
the $L$orbital
measures supported on the orbits generated by the $X_{i}$ is
absolutely continuous and, equivalently, the sum of their orbits
has
nonempty interior. The characterization depends on the Lie type
of
$\mathfrak{g}$ and the structure of the annihilating roots of
the $X_{i}$.
Such a characterization was previously known only for type $A_{n}$.
Keywords:compact Lie algebra, orbital measure, absolutely continuous measure Categories:43A80, 17B45, 58C35 

2. CJM 2000 (vol 52 pp. 412)
 Varopoulos, N. Th.

Geometric and Potential Theoretic Results on Lie Groups
The main new results in this paper are contained in the geometric
Theorems 1 and~2 of Section~0.1 below and they are related to
previous results of M.~Gromov and of myself (\cf\
\cite{1},~\cite{2}). These results are used to prove some general
potential theoretic estimates on Lie groups (\cf\ Section~0.3) that
are related to my previous work in the area (\cf\
\cite{3},~\cite{4}) and to some deep recent work of G.~Alexopoulos
(\cf\ \cite{5},~\cite{21}).
Categories:22E30, 43A80, 60J60, 60J65 

3. CJM 1998 (vol 50 pp. 1090)