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Quasigeodesics and farthest points on convex surfaces
-
K. Ieiri
,
J. Itoh
Published/Copyright:
August 19, 2011
Abstract
We prove a quadrilateral comparison result for convex surfaces, involving projections onto quasigeodesics. As an application, we locate the set of all farthest points (i.e., points at maximal intrinsic distance from some point) in a convex surface, with respect to a simple closed quasigeodesic.
Received: 2007-06-06
Revised: 2008-02-11
Revised: 2008-02-02
Published Online: 2011-08-19
Published in Print: 2011-November
© de Gruyter 2011
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Articles in the same Issue
- Quasigeodesics and farthest points on convex surfaces
- The geometry of canal surfaces and the length of curves in de Sitter space
- On the mutual position of two irreducible conics in PG(2, q), q odd
- On the symmetric average of a convex body
- Ample vector bundles and polarized manifolds of sectional genus three
- Flat Laguerre planes of Kleinewillinghöfer type III.B
- Quotients of hypersurfaces in weighted projective space
- Characterizing the mixed volume
- Uniqueness of lattice packings and coverings of extreme density
- On the classification of convex lattice polytopes
- Blichfeldt-type inequalities and central symmetry
- Valuations on function spaces
