This paper describes sufficient conditions under which a biconcave function
B
:
S
=
{
(
x
,
y
)
∈
R
2
:
x
−
2
≤
y
≤
x
+
2
}
→
R
\mathcal {B}\colon \mathfrak {S}=\{ (x,y)\in \mathbb {R}^2\colon x-2\le y\le x+2 \}\to \mathbb {R}
is minimal with respect to an obstacle
L
:
S
→
[
−
∞
,
+
∞
)
L\colon \mathfrak {S}\to [-\infty ,+\infty )
, that is, it is the pointwise minimal among all biconcave functions
B
:
S
→
R
B\colon \mathfrak {S}\to \mathbb {R}
that satisfy the inequality
B
≥
L
B\ge L
.