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Minimal area conics in the elliptic plane
-
Matthias J. Weber
and
Hans-Peter Schröcker
Published/Copyright:
December 11, 2012
Abstract
We prove uniqueness results for conics of minimal area that enclose a compact, fulldimensional 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.
Keywords: Minimal conic; sphero-conic; spherical ellipse; covering cone; elliptic geometry; spherical geometry; enclosing conic; uniqueness.
Published Online: 2012-12-11
Published in Print: 2012-10
© 2012 by Walter de Gruyter GmbH & Co.
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Keywords for this article
Minimal conic;
sphero-conic;
spherical ellipse;
covering cone;
elliptic geometry;
spherical geometry;
enclosing conic;
uniqueness.
Articles in the same Issue
- Masthead
- Barycenters in Alexandrov spaces of curvature bounded below
- Isoperimetric problems in sectors with density
- Around A. D. Alexandrov’s uniqueness theorem for convex polytopes
- A relative isoperimetric inequality for certain warped product spaces
- Markov’s inequality in the o-minimal structure of convergent generalized power series
- Minimal area conics in the elliptic plane
- Geometry of semi-tube domains in ℂ2
- Flag transitive c:F4(2)-geometries
- Majorana representations of L3(2)
- A characterization of multiple (n – k)-blocking sets in projective spaces of square order
