  This work considers the corner points of the capacity region of a two-user
Gaussian interference channel (GIC). In a two-user GIC, the rate pairs where
one user transmits its data at the single-user capacity (without interference),
and the other at the largest rate for which reliable communication is still
possible are called corner points. This paper relies on existing outer bounds
on the capacity region of a two-user GIC that are used to derive informative
bounds on the corner points of the capacity region. The new bounds refer to a
weak two-user GIC (i.e., when both cross-link gains in standard form are
positive and below 1), and a refinement of these bounds is obtained for the
case where the transmission rate of one user is within $\varepsilon > 0$ of the
single-user capacity. The bounds on the corner points are asymptotically tight
as the transmitted powers tend to infinity, and they are also useful for the
case of moderate SNR and INR. Upper and lower bounds on the gap (denoted by
$\Delta$) between the sum-rate and the maximal achievable total rate at the two
corner points are derived. This is followed by an asymptotic analysis analogous
to the study of the generalized degrees of freedom (where the SNR and INR
scalings are coupled such that $\frac{\log(\text{INR})}{\log(\text{SNR})} =
\alpha \geq 0$), leading to an asymptotic characterization of this gap which is
exact for the whole range of $\alpha$. The upper and lower bounds on $\Delta$
are asymptotically tight in the sense that they achieve the exact asymptotic
characterization. Improved bounds on $\Delta$ are derived for finite SNR and
INR, and their improved tightness is exemplified numerically.
