  We use a renormalized mean field theory to investigate the superconducting
properties of underdoped cuprates embedded with overdoped or metallic regions
that carry excess dopants. The overdoped regions are considered, within two
different models, first as stripes of mesoscopic size larger than the coherence
length and then as point impurities. In the former case we compute the
temperature dependent superfluid stiffness by solving Bogoliubov de Gennes
equations within the slave boson mean field theory. We average over stripes of
different orientations to obtain an isotropic result. To compute the superfluid
stiffness in the model with point impurities we resort to a diagrammatic
expansion in the impurity concentration (to first order) and their strength (up
to second order). We find analytic expressions for the disorder averaged
superfluid stiffness and the critical temperature. For both types of
inhomogeneity we find increased superfluid stiffness, and for a wide range of
doping enhancement of Tc relative to a homogeneously underdoped system.
Remarkably, in the case of microscopic impurities we find that the maximal Tc
can be significantly increased compared to Tc at optimal doping of a pure
system.
