  In this note we pursue a discrete analogue of a celebrated theorem by Osgood,
Phillips and Sarnak, which states that in a fixed conformal class of Riemannian
metrics of fixed volume on a closed Riemann surface, the zeta-determinant of
the corresponding Laplace-Beltrami operator is maximized on a metric of
constant Gaussian curvature. We study the corresponding question for the
discrete cotan Laplace operator on triangulated surfaces. We show for some
types of triangulations that the determinant (excluding zero eigenvalues) of
the discrete cotan-Laplacian is stationary at discrete metrics of constant
discrete Gaussian curvature. We present some numerical calculations, which
suggest that these stationary points are in fact minima, strangely opposite to
the smooth situation. We suggest an explanation of this discrepancy.
