https://en.formulasearchengine.com/api.php?action=feedcontributions&feedformat=atom&user=132.76.61.23formulasearchengine - User contributions [en]2026-05-02T04:50:30ZUser contributionsMediaWiki 1.43.0-wmf.28https://en.formulasearchengine.com/index.php?title=Backfitting_algorithm&diff=24891Backfitting algorithm2013-07-18T07:14:40Z<p>132.76.61.23: /* Motivation */</p>
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<div>{{Orphan|date=February 2013}}<br />
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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]].<br />
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==Formulation==<br />
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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<br />
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: <math>t\mapsto\operatorname{dist}^2\circ\gamma(t)-t^2 \, </math><br />
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is concave.<br />
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==References==<br />
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*Liberman, J. Geodesic lines on convex surfaces. C. R. (Doklady) Acad. Sci. URSS (N.S.) 32, (1941). 310&ndash;313.<br />
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[[Category:Differential geometry of surfaces]]<br />
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{{differential-geometry-stub}}</div>132.76.61.23