A conjecture on convex polyhedra.
A measure of asymmetry for domains of constant width.
A measure of axial symmetry of centrally symmetric convex bodies
Denote by Kₘ the mirror image of a planar convex body K in a straight line m. It is easy to show that K*ₘ = conv(K ∪ Kₘ) is the smallest by inclusion convex body whose axis of symmetry is m and which contains K. The ratio axs(K) of the area of K to the minimum area of K*ₘ over all straight lines m is a measure of axial symmetry of K. We prove that axs(K) > 1/2√2 for every centrally symmetric convex body and that this estimate cannot be improved in general. We also give a formula for axs(P) for...
A quantitative isoperimetric inequality in n-dimensional space.
A representation for volume involving interior reach.
A reverse isoperimetric inequality for convex plane curves.
A sufficient condition for the convexity of the area of an isoptic curve of an oval
About an inequality of Kubota for plane convex figures.
Almost sure asymptotic behaviour of the -neighbourhood surface area of Brownian paths
We show that whenever the -dimensional Minkowski content of a subset exists and is finite and positive, then the “S-content” defined analogously as the Minkowski content, but with volume replaced by surface area, exists as well and equals the Minkowski content. As a corollary, we obtain the almost sure asymptotic behaviour of the surface area of the Wiener sausage in , .
An Equipartition of Planar Sets.
An isoperimetric partition problem.
Approximation of spherical caps by polygons
Approximation of Zonoids by Zonotopes in Fixed Directions.
Area and coarea formulas for the mappings of Sobolev classes with values in a metric space.
Areas of lattice polygons, applied to computer graphics
Areas of Polygons Inscribed in a Circle.
Balancing vectors and convex bodies
Let U, V be two symmetric convex bodies in and |U|, |V| their n-dimensional volumes. It is proved that there exist vectors such that, for each choice of signs , one has where . Hence it is deduced that if a metrizable locally convex space is not nuclear, then it contains a null sequence such that the series is divergent for any choice of signs and any permutation π of indices.
Clusters minimizing area plus length of singular curves.
Comparing the relative volume with the relative inradius and the relative width.
Complete systems of inequalities.