120713975
Eine allgemeine Extremaleigenschaft der Kugel
26498631
Isoperimetric inequalities for infinite hyperplane systems
Let be an infinite discrete system ofk-dimensional flats inn-dimensional Euclidean space. If the totalk-dimensional volume of the flats in intersected with the ball of center 0 and radiusr, divided by the volume of that ball, tends to a limit forr→∞, then this limit is called thedensity of. We consider isoperimetric problems of the following kind. If is a hyperplane system of positive density, find sharp upper bounds for the density of the system ofk-flats (k∈{0, ...,n−2}) that are generated as intersections of hyperplanes in. Ideas from the theory of uniform distribution of sequences are employed to define a large class of hyperplane systems, calleduniform, for which all necessary densities exist, isperimetric inequalities can be proved, and systems with extremal intersection densities can be characterized.
120667836
Characterization of certain polytopes by intersection properties of their translates
124345785
A Characteristic Property of the Ellipsoid
123088657
On steiner points of convex bodies
Ifs is a mapping from the set of all convex bodies in Euclidean spaceEd toEd which is additive (in the sense of Minkowski), equivariant with respect to proper motions, and continuous, thens(K) is the Steiner point of the convex bodyK.
122254313
On the projections of a convex polytope
120014020
Stability of a spline collocation method for strongly elliptic multidimensional singular integral equations
SummaryWe consider a spline collocation method for strongly elliptic zero order pseudodifferential equationspgwAu=f on a cube ω=(0, 1)m. Utilizing multilinear spline functions which are zero at the boundary σω we collocate at the meshpoints inside ω. For classical strongly elliptic translation invariant pseudodifferential operators, we verify the stability of the considered collocation method inL2(ω). Afterwards, form≦2 and a right hand sidef∈H8(ω),s>m/2, we prove an asymptotic convergence estimate.