Inverse cartographic problems: theory and first results

In view of the anniversary of Martin Hotine, the authors have thought to honour his memory writing a paper on a subject related to one of his favourite items, namely the problems of map representations. The point of view which is pursued here however is non-traditional and follows some research conducted at Politecnico di Milano, joining the problems of various types of representations between different surfaces with the peculiar theory of the so-called inverse problems. We hope that the material presented here, will be interesting enough to reach the goal that the authors have in mind.