In this paper we characterize the degenerate elliptic equations F(D2u) = 0
whose subsolutions (F(D2u) = 0) satisfy the strong maximum principle. We introduce
an easily computed function f on (0,1) which is determined by F, and we show that
the strong maximum principle holds depending on whether
R
0+
dy
f(y) is infinite or finite.
This is in the spirit of previous work characterizing the ordinary maximum principle in
terms of the geometry of the set of symmetric matrices F = {F = 0}. Along the way,
radial subsolutions are characterized, and, as an application, a sufficient condition for
strong comparison is established. A number of examples, important for the theory of such
equations, are examined.