Minimal area conics in the elliptic plane

2010/08/25 by Matthias J. Weber, Weber, Matthias J., Hans-Peter Schröcker +1 · 1 citation
Mathematics · #51M10 (Secondary) #52A40 (Primary) 52A55 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:51M10 #msc:52A40 #msc:52A55

paper · pdf · doi:10.48550/arxiv.1008.4285

arxiv created 2010/08/25 · arxiv updated 2010/08/26

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.

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• Uniqueness of Maximal Inscribed Parabolas and Minimal Circumscribing Horocycles

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