Backfitting algorithm: Difference between revisions

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{{Orphan|date=February 2013}}
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In the [[differential geometry]] of [[surface]]s, '''Liberman's lemma''' is key tool in studying [[intrinsic metric|intrinsic geometry]] of [[convex surface]].
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==Formulation==
 
If <math>\gamma</math> is a unit-speed minimizing [[geodesic]] on the surface of a [[convex body]] ''K'' in [[Euclidean space]] then for any point ''p''&nbsp;&isin;&nbsp;''K'', the function
 
: <math>t\mapsto\operatorname{dist}^2\circ\gamma(t)-t^2 \, </math>
 
is concave.
 
==References==
 
*Liberman, J. Geodesic lines on convex surfaces. C. R. (Doklady) Acad. Sci. URSS (N.S.) 32, (1941). 310&ndash;313.
 
[[Category:Differential geometry of surfaces]]
 
 
{{differential-geometry-stub}}

Latest revision as of 15:13, 26 August 2014

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