Abstract
The paper studies the relation between the asymptotic values of the ratios area/length (F/L) and diameter/length (D/L) of a sequence of convex sets expanding over the whole hyperbolic plane. It is known that F/L goes to a value between 0 and 1 depending on the shape of the contour. In the paper, it is first of all seen that D/L has limit value between 0 and 1/2 in strong contrast with the euclidean situation in which the lower bound is 1/π (D/L = 1/π if and only if the convex set has constant width). Moreover, it is shown that, as the limit of D/L approaches 1/2, the possible limit values of F/L reduce. Examples of all possible limits F/L and D/L are given.
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.
