Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
Let K be a convex body in $ℝ^n$ and B be the Euclidean unit ball in $ℝ^n$. We show that $lim_{t→ 0} (|K| -|K_t|)/(|B| - |B_t|) = as(K)/as(B)$, where as(K) respectively as(B) is the affine surface area of K respectively B and ${K_t}_{t≥0}$, ${B_t}_{t≥0}$ are general families of convex bodies constructed from K,B satisfying certain conditions. As a corollary we get results obtained in [M-W], [Schm], [S-W] and [W].
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
227-238
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-06-30
otrzymano
1998-05-20
Twórcy
autor
- Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106, U.S.A., emw2@po.cwru.edu
- Université de Lille 1, UFR de Mathématique, 59699 Villeneuve d'Ascq, France
Bibliografia
- [B] W. Blaschke, Vorlesungen über Differentialgeometrie II: Affine Differentialgeometrie, Springer, 1923.
- [Gr] P. Gruber, Aspects of approximation of convex bodies, in: Handbook of Convex Geometry, Vol. A, North-Holland, 1993, 321-345.
- [K] K. Kiener, Extremalität von Ellipsoiden und die Faltungsungleichung von Sobolev, Arch. Math. (Basel) 46 (1986), 162-168.
- [L1] K. Leichtweiss, Zur Affinoberfläche konvexer Körper, Manuscripta Math. 56 (1986), 429-464.
- [L2] K. Leichtweiss, Über ein Formel Blaschkes zur Affinoberfläche, Studia Sci. Math. Hungar. 21 (1986), 453-474.
- [Lu] E. Lutwak, Extended affine surface area, Adv. Math. 85 (1991), 39-68.
- [Lu-O] E. Lutwak and V. Oliker, On the regularity of solutions to a generalization of the Minkowski problem, J. Differential Geometry 41 (1995), 227-246.
- [M-W] M. Meyer and E. Werner, The Santaló regions of a convex body, Trans. Amer. Math. Soc., to appear.
- [Schm] M. Schmuckenschläger, The distribution function of the convolution square of a convex symmetric body in $ℝ^n$, Israel J. Math. 78 (1992), 309-334.
- [S] C. Schütt, Floating body, illumination body, and polytopal approximation, preprint.
- [S-W] C. Schütt and E. Werner, The convex floating body, Math. Scand. 66 (1990), 275-290.
- [W] E. Werner, Illumination bodies and affine surface area, Studia Math. 110 (1994), 257-269.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv132i3p227bwm