  We consider mappings of domains of Riemannian manifolds that admit branch
points and satisfy a certain condition regarding the distortion of the modulus
of families of paths. We have established logarithmic estimates of distance
distortion under such mappings. A separate study relates to the situation when
the mappings are defined in metric spaces, and one of them is the Loewner
space. We also studied the question of equicontinuity of the families of the
indicated mappings in the closure of the domain. In addition, we have
established the possibility of continuous extension of these mappings to an
isolated point of the boundary.
