Sections of Convex Bodies in John’s and Minimal Surface Area Position

Abstract We prove several estimates for the volume, the mean width, and the value of the Wills functional of sections of convex bodies in John’s position, as well as for their polar bodies. These estimates extend some well-known results for convex bodies in John’s position to the case of lower-dimensional sections, which had mainly been studied for the cube and the regular simplex. Some estimates for centrally symmetric convex bodies in minimal surface area position are also obtained.

Comparing the M-position with some classical positions of convex bodies

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004111000703 ◽

2011 ◽

Vol 152 (1) ◽

pp. 131-152 ◽

Cited By ~ 3

Author(s):

E. MARKESSINIS ◽

G. PAOURIS ◽

CH. SAROGLOU

Keyword(s):

Minimal Surface ◽

Surface Area ◽

Convex Bodies ◽

Mean Width ◽

Quantitative Results ◽

AbstractThe purpose of this paper is to compare some classical positions of convex bodies. We provide exact quantitative results which show that the minimal surface area position and the minimal mean width position are not necessarily M-positions. We also construct examples of unconditional convex bodies of minimal surface area that exhibit the worst possible behavior with respect to their mean width or their minimal hyperplane projection.

Application of Raman Spectroscopy to the Study of Adsorption Effects at Liquid-Solid Interfaces

Applied Spectroscopy ◽

10.1366/0003702824639637 ◽

1982 ◽

Vol 36 (4) ◽

pp. 471-473 ◽

Cited By ~ 5

Author(s):

Klaus Witke

Keyword(s):

Raman Spectroscopy ◽

Carbon Tetrachloride ◽

Adsorption Isotherm ◽

Minimal Surface ◽

Linear Relationship ◽

Surface Area ◽

Long Range ◽

Raman Spectra ◽

Sample Cell ◽

A sample cell for investigating suspensions or emulsions by Raman spectroscopy in the optically favorable 90° scattering arrangement is described. The Raman spectra of pyridine in a suspension of Aerosil 200 in carbon tetrachloride are recorded. The adsorption isotherm of pyridine is determined from the intensities of the Raman lines at 1008 and 990 cm−1. Over a long range of coverage a linear relationship exists between reciprocal concentrations of chemisorbed and dissolved molecules. The minimal surface area that is occupied by a chemisorbed molecule is determined to be approximately 0.75 nm2.

Convex Bodies of Minimal Volume, Surface Area and Mean Width with Respect to Thin Shells

Canadian Journal of Mathematics ◽

10.4153/cjm-2008-001-x ◽

2008 ◽

Vol 60 (1) ◽

pp. 3-32 ◽

Cited By ~ 1

Author(s):

Károly Böröczky ◽

Károly J. Böröczky ◽

Carsten Schütt ◽

Gergely Wintsche

Keyword(s):

Unit Ball ◽

Surface Area ◽

Convex Bodies ◽

Extreme Points ◽

Thin Shells ◽

Minimal Volume ◽

Asymptotic Formulae ◽

Mean Width

AbstractGiven r > 1, we consider convex bodies in En which contain a fixed unit ball, and whose extreme points are of distance at least r from the centre of the unit ball, and we investigate how well these convex bodies approximate the unit ball in terms of volume, surface area and mean width. As r tends to one, we prove asymptotic formulae for the error of the approximation, and provide good estimates on the involved constants depending on the dimension.

A measure of axial symmetry of centrally symmetric convex bodies

Colloquium Mathematicum ◽

10.4064/cm121-2-12 ◽

2010 ◽

Vol 121 (2) ◽

pp. 295-306 ◽

Cited By ~ 1

Author(s):

Marek Lassak ◽

Monika Nowicka

Keyword(s):

Axial Symmetry ◽

Convex Bodies ◽

Symmetric Convex ◽

A characterization of centrally symmetric convex bodies in En

Geometriae Dedicata ◽

10.1007/bf01447420 ◽

1981 ◽

Vol 10 (1-4) ◽

pp. 161-176 ◽

Cited By ~ 5

Author(s):

D. G. Larman ◽

N. K. Tamvakis

Keyword(s):

Convex Bodies ◽

Symmetric Convex ◽

Tensor product surfaces guided by minimal surface area triangulations

Proceedings Visualization '95 ◽

10.1109/visual.1995.480820 ◽

2002 ◽

Cited By ~ 5

Author(s):

J.K. Johnstone ◽

K.R. Sloan

Keyword(s):

Tensor Product ◽

Minimal Surface ◽

Surface Area ◽

Some problems concerning centrally symmetric convex bodies

Journal of Soviet Mathematics ◽

10.1007/bf01476853 ◽

1978 ◽

Vol 10 (3) ◽

pp. 454-460

Author(s):

V. A. Zalgaller ◽

V. N. Sudakov

Keyword(s):

Convex Bodies ◽

Symmetric Convex ◽

On the Busemann-Petty problem\\ concerning central sections\\ of centrally symmetric convex bodies

Bulletin of the American Mathematical Society ◽

10.1090/s0273-0979-1994-00493-8 ◽

1994 ◽

Vol 30 (2) ◽

pp. 222-227 ◽

Cited By ~ 14

Author(s):

R. J. Gardner

Keyword(s):

Convex Bodies ◽

Symmetric Convex ◽

Black-Silicon on Micropillars with Minimal Surface Area Enlargement to Enhance the Performance of Silicon Solar Cells

nano Online ◽

10.1515/nano.s11671-016-1716-y ◽

2017 ◽

Author(s):

Jiann Shieh ◽

Chengyun You ◽

Chiachen Chiu ◽

Jianming Liu ◽

Pingyu Shih

Keyword(s):

Solar Cells ◽

Minimal Surface ◽

Surface Area ◽

Silicon Solar Cells ◽

Black Silicon ◽

Centrally symmetric convex bodies and sections having maximal quermassintegrals

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.49.2012.2.1197 ◽

2012 ◽

Vol 49 (2) ◽

pp. 189-199

Author(s):

E. Makai ◽

H. Martini

Keyword(s):

Convex Body ◽

Convex Bodies ◽

The Body ◽

Symmetric Convex ◽

Local Theorem ◽

Centrally Symmetric ◽

Euclidean Unit Ball ◽

Analogous Theorem ◽

Lower Dimensional ◽

Dimensional Surface

Let d ≧ 2, and let K ⊂ ℝd be a convex body containing the origin 0 in its interior. In a previous paper we have proved the following. The body K is 0-symmetric if and only if the following holds. For each ω ∈ Sd−1, we have that the (d − 1)-volume of the intersection of K and an arbitrary hyperplane, with normal ω, attains its maximum if the hyperplane contains 0. An analogous theorem, for 1-dimensional sections and 1-volumes, has been proved long ago by Hammer (see [2]). In this paper we deal with the ((d − 2)-dimensional) surface area, or with lower dimensional quermassintegrals of these intersections, and prove an analogous, but local theorem, for small C2-perturbations, or C3-perturbations of the Euclidean unit ball, respectively.