Balls in the triangular ratio metric
Sami Hokuni, Riku Kl\'en, Yaxiang Li, Matti Vuorinen
TL;DR
This paper investigates the properties of the triangular ratio metric, estimating the convexity radius of its balls in specific domains and exploring their inclusion relations with other well-known metrics.
Contribution
It provides new estimates for the convexity radius of metric balls and establishes inclusion relations among balls defined by different metrics.
Findings
Estimated the radius of convexity for balls in specific domains.
Proved inclusion relations among triangular ratio, quasihyperbolic, and j-metric balls.
Abstract
We consider the triangular ratio metric and estimate the radius of convexity for balls in some special domains and prove the inclusion relations of metric balls defined by the triangular ratio metric, the quasihyperbolic metric and the -metric.
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
TopicsAnalytic and geometric function theory · Point processes and geometric inequalities · Geometric Analysis and Curvature Flows