  We proposed a six dimensional string-like braneworld built from a warped
product between a 3-brane and the Hamilton cigar soliton space, the
string-cigar braneworld. This transverse manifold is a well-known steady
solution of the Ricci flow equation that describes the evolution of a manifold.
The resulting bulk is an interior and exterior metric for a thick string. This
is a physical and feasible scenario since the source satisfies the dominant
energy condition. It is possible to realize the geometric flow as a result of
variations of the matter content of the brane, actually, as its tensions.
Furthermore, the Ricci flow defines a family of string-like branes and we
studied the effects that the evolution of the transverse space has on the
geometric and physical quantities. The geometric flow makes the cosmological
constant and the relationship between the Planck masses evolves. The
gravitational massless mode remains trapped to the brane and the width of the
mode depends on the evolution parameter. For the Kaluza-Klein modes, the
asymptotic spectrum of mass is the same as for the thin string-like brane and
the analogue Schroedinger potential also changes according to the flow.
