Let S denote the set of functions
f
(
z
)
f(z)
analytic and univalent in
|
z
|
>
1
|z|\, > \,1
, normalized by
f
(
0
)
=
0
f(0)\, = \,0
and
f
′
(
0
)
=
1
f’(0)\, = \,1
. A function f is a support point of S if there exists a continuous linear functional L, nonconstant on S, for which f maximizes Re
Re
L
(
g
)
\operatorname {Re} \,L(g)
,
g
∈
S
g \in S
. The support points corresponding to the point-evaluation functionals are determined explicitly and are shown to also be extreme points of S. New geometric properties of their omitte
arcs
Γ
\operatorname {arcs}\,\Gamma
are found. In particular, it is shown that for each such support point
Γ
\Gamma
lies entirely in a certain half-strip,
Γ
\Gamma
has monotonic argument, and the angle between radius and tangent vectors increases from zero at infinity to a finite maximum value at the tip of the
arc
Γ
\operatorname {arc}\,\Gamma
. Numerical calculations appear to indicate that the known bound
π
/
4
\pi /4
for the angle between radius and tangent vectors is actually best possible.