Minimal area ellipses in the hyperbolic plane
Matthias J. Weber, Hans-Peter Schr\"ocker
TL;DR
This paper investigates the problem of finding the smallest-area ellipses that enclose a given set in the hyperbolic plane, providing conditions for uniqueness and criteria for the general case.
Contribution
It introduces new uniqueness results for minimal area ellipses in hyperbolic geometry, including criteria that guarantee uniqueness in the general case.
Findings
Uniqueness of minimal area ellipses with prescribed axes or center
A sufficient criterion for uniqueness in the general case
Conditions under which minimal ellipses are uniquely determined
Abstract
We present uniqueness results for enclosing ellipses of minimal area in the hyperbolic plane. Uniqueness can be guaranteed if the minimizers are sought among all ellipses with prescribed axes or center. In the general case, we present a sufficient and easily verifiable criterion on the enclosed set that ensures uniqueness.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematics and Applications · Point processes and geometric inequalities · Analytic Number Theory Research