John and Loewner Ellipsoids
نویسندگان
چکیده
منابع مشابه
Löwner-john Ellipsoids
Before giving the mathematical description of the Löwner-John ellipsoids and pointing out some of their far-ranging applications, I briefly illuminate the adventurous life of the two eminent mathematicians, by whom the ellipsoids are named: Charles Loewner (Karel Löwner) and Fritz John. Karel Löwner was born into a Jewish family in Lány, a small town about 30 km west of Prague, in 1893. Due to ...
متن کاملVOLUME INEQUALITIES FOR Lp-JOHN ELLIPSOIDS AND THEIR DUALS
In this paper, we establish some inequalities among the Lp-centroid body, the Lp-polar projection body, the Lp-John ellipsoid and its dual, which are the strengthened version of known results. We also prove inequalities among the polar of the Lp-centroid body, the Lp-polar projection body, the Lp-John ellipsoid and its dual. 2000 Mathematics Subject Classification. 52A40, 52A20.
متن کاملLoewner Matrices and Operator Convexity
Let f be a function from R+ into itself. A classic theorem of K. Löwner says that f is operator monotone if and only if all matrices of the form [ f(pi)−f(pj) pi−pj ] are positive semidefinite. We show that f is operator convex if and only if all such matrices are conditionally negative definite and that f(t) = tg(t) for some operator convex function g if and only if these matrices are conditio...
متن کاملHyperelliptic Surfaces Are Loewner
We prove that C. Loewner’s inequality for the torus is satisfied by conformal metrics on hyperelliptic surfaces X , as well. In genus 2, we first construct the Loewner loops on the (mildly singular) companion tori, locally isometric to X away from Weierstrass points. The loops are then transplanted to X , and surgered to obtain a Loewner loop on X . In higher genus, we exploit M. Gromov’s area ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2011
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-011-9354-8