Complete Laguerre minimal surfaces in R3

We study from a global point of view the Laguerre minimal surfaces in R3R3. In particular, we generalize in a natural way the class of Laguerre minimal surfaces (introducing what we call Generalized Laguerre minimal surfaces) and obtain a conformal representation formula for this new class of surfaces. Besides, we study the completeness of the Laguerre metric and classify the flat Laguerre minimal surfaces. Finally, we solve the Björling problem for Generalized Laguerre minimal surfaces and, as an application, we classify the rotational ones.