Laguerre minimal surfaces in \(\mathbb R^{3}\) (Q960614)

The authors relate generic Laguerre minimal surfaces to solutions of the Liouville equation, thus providing a way to obtain generic Laguerre minimal surfaces from holomorphic data. In the degenerate case, the authors relate Laguerre minimal surfaces to surfaces with vanishing mean curvature in a degenerate space. They prove that every Laguerre minimal surface with constant curvature of the induced metric of the ``mean curvature radii congruence'', an analogue of the central sphere congruence of Möbius geometry, is degenerate in the above sense, thus related to a zero mean curvature surface in a degenerate ambient geometry.