  Tumor growth has a number of features in common with a physical process known
as molecular beam epitaxy. Both growth processes are characterized by the
constraint of growth development to the body border, and surface diffusion of
cells/particles at the growing edge. However, tumor growth implies an
approximate spherical symmetry that makes necessary a geometrical treatment of
the growth equations. The basic model was introduced in a former article [C.
Escudero, Phys. Rev. E 73, 020902(R) (2006)], and in the present work we extend
our analysis and try to shed light on the possible geometrical principles that
drive tumor growth. We present two-dimensional models that reproduce the
experimental observations, and analyse the unexplored three-dimensional case,
for which new conclusions on tumor growth are derived.
