  Consider a memoryless relay channel, where the relay is connected to the
destination with an isolated bit pipe of capacity $C_0$. Let $C(C_0)$ denote
the capacity of this channel as a function of $C_0$. What is the critical value
of $C_0$ such that $C(C_0)$ first equals $C(\infty)$? This is a long-standing
open problem posed by Cover and named "The Capacity of the Relay Channel," in
$Open \ Problems \ in \ Communication \ and \ Computation$, Springer-Verlag,
1987. In this paper, we answer this question in the Gaussian case and show that
$C(C_0)$ can not equal to $C(\infty)$ unless $C_0=\infty$, regardless of the
SNR of the Gaussian channels. This result follows as a corollary to a new upper
bound we develop on the capacity of this channel. Instead of
"single-letterizing" expressions involving information measures in a
high-dimensional space as is typically done in converse results in information
theory, our proof directly quantifies the tension between the pertinent
$n$-letter forms. This is done by translating the information tension problem
to a problem in high-dimensional geometry. As an intermediate result, we
develop an extension of the classical isoperimetric inequality on a
high-dimensional sphere, which can be of interest in its own right.
