Minimal area conics in the elliptic plane

TL;DR

This paper establishes uniqueness conditions for minimal area conics enclosing sets in the elliptic plane, including cases with prescribed centers or axes, and extends results to line sets.

Contribution

It provides new uniqueness theorems for minimal enclosing conics in the elliptic plane, with and without restrictions on the conics.

Findings

Uniqueness of minimal conics with prescribed center or axes.

Sufficient conditions for uniqueness without restrictions.

Extension of results to line sets.

Abstract

We prove some uniqueness results for conics of minimal area that enclose a compact, full-dimensional subset of the elliptic plane. The minimal enclosing conic is unique if its center or axes are prescribed. Moreover, we provide sufficient conditions on the enclosed set that guarantee uniqueness without restrictions on the enclosing conics. Similar results are formulated for minimal enclosing conics of line sets as well.