  We introduce a technique to estimate a linear operator by embedding it in a
family $A_t$ of operators, $t\in(\sigma_0,\infty)$, with suitable curvature
properties. One can then estimate the norm of each $A_t$ by bounds that hold in
the limit $t\to\sigma_0$, respectively, $t\to\infty$. We illustrate this
technique on an extension problem that arises in complex geometry.
