We study the asymptotic Dirichlet problem for the minimal graph equation on a Cartan–Hadamard manifold
M whose radial sectional curvatures outside a compact set satisfy an upper bound
$$\begin{aligned} K(P)\le - \frac{\phi (\phi -1)}{r(x)^2} \end{aligned}$$
and a pointwise pinching condition
$$\begin{aligned} |K(P) |\le C_K|K(P') | \end{aligned}$$
for some constants
\(\phi >1\) and
\(C_K\ge 1\), where
P and
\(P'\) are any 2-dimensional subspaces of
\(T_xM\) containing the (radial) vector
\(\nabla r(x)\) and
\(r(x)=d(o,x)\) is the distance to a fixed point
\(o\in M\). We solve the asymptotic Dirichlet problem with any continuous boundary data for dimensions
\(n=\dim M>4/\phi +1\).