  We study the tubular phase of self-avoiding anisotropic membranes. We discuss
the renormalizability of the model Hamiltonian describing this phase and derive
from a renormalization group equation some general scaling relations for the
exponents of the model. We show how particular choices of renormalization
factors reproduce the Gaussian result, the Flory theory and the Gaussian
Variational treatment of the problem. We then study the perturbative
renormalization to one loop in the self-avoiding parameter using dimensional
regularization and an epsilon-expansion about the upper critical dimension, and
determine the critical exponents to first order in epsilon.
