  The field equations associated to Born-Infeld type brane theories are studied
by using an auxiliary variables method. This approach hinges on the fact that
the expressions defining the physical and geometrical quantities describing the
worldvolume are varied independently. The general structure of the Born-Infeld
type theories for branes contains the square root of a determinant of a
combined matrix between the induced metric on the worldvolume swept out by the
brane and a symmetric/antisymmetric tensor depending of gauge, matter or
extrinsic curvature terms taking place on the worldvolume. The higher order
curvature terms appearing in the determinant form come to play as competition
with other effective brane models. Additionally, we suggest a
Born-Infeld-Einstein type action for branes where the higher order curvature
content is provided by the worldvolume Ricci tensor. This action provide an
alternative description of the dynamics of braneworld scenarios.
