Abstract
One considers the modulus problem for a family of homotopic classes {Hi}, in the extended complex plane , of the following types. The classes Hn consist of closed Jordan curves, homotopic to appropriate nondegenerate contours or point curves, and also of arcs with endpoints in (distinct or coinciding) distinguished points in . One establishes the relation of the indicated extremal metric problem and the problem on the extremal decomposition of in the family of systems of mutually nonoverlapping domains {Di}, associated with the family of the classes {Hi}. The results of this paper complement a previous theorem of the author [Moduli of families of curves and quadratic differentials. Trudy Mat. Inst. Akad. Nauk SSSR, Vol. 139, 1980].
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
