the comparison may require the knowledge of the complete development in time of their solutions near the boundary and the subsequent calculation of a gauge transformation on the boundary.

It is the purpose of this article to illustrate the difficulties to arrive at an appropriate concept of geometric uniqueness in the context of general initial boundary value problems. Whether they will find a natural resolution or whether we will have to live with them remains an open question. At the end of the article we discuss a natural and important class of initial boundary value problems which seem to offer a chance for a positive answer.

Some observations
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The following [*flat, linear model problem*]{} is the prototype of an initial boundary value problem for a hyperbolic equation. In terms of coordinates $x^{\mu}$ on Minkowski space in which $g_{\mu \nu} = \eta_{\mu \nu} \equiv diag(-1, 1, 1, 1)$ we consider the wave equation $$g^{\mu \nu}\,\phi_{,\,\mu \nu} = f \quad \mbox{on} \quad {\cal M} = \{t \ge 0, |x| \le R\},$$ where $t = x^0$, $R  = const. > 0$, and $|x| = \sqrt{\sum_{a = 1}^3 (x^a)^2}$. We prescribe initial conditions $$\phi = \phi_0, \quad \partial_t\,\phi = \phi_1 \quad \mbox{on} \quad   