On some degenerate elliptic equations arising in geometrical problems

We consider some fully nonlinear degenerate elliptic operators and we investigate the validity of certain properties related to the maximum principle. In particular, we establish the equivalence between the sign propagation property and the strict positivity of a suitably dened generalized principal eigenvalue. Furthermore, we show that even in the degenerate case considered in the present paper, the well-known condition introduced by Keller{Osserman on the zero order term is necessary and sucient for the existence of entire weak subsolutions.