Abstract.
In this study the problem of finding the conformal mapping from a sphere onto a plane with a given scale function independent of longitude is solved for an arbitrary spherical domain. The obtained results are compared with the well-known projections used in cartography and geophysical fluid dynamics. The problem of minimization of the distortion under conformal mappings is solved for domains in the form of the spherical disk. The distortions of some extensively used conformal mappings are compared with the distortions of orthogonal mappings.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bourchtein, A., Bourchtein, L. Some problems of conformal mappings of spherical domains. Z. angew. Math. Phys. 58, 926–939 (2007). https://doi.org/10.1007/s00033-006-5126-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00033-006-5126-3