TheNontrivial Projection Problem asks whether every finite-dimensional normed space admits a well-bounded projection of non-trivial rank and corank or, equivalently, whether every centrally symmetric convex body (of arbitrary dimension) is approximately affinely equivalent to a direct product of two bodies of non-trivial dimension. We show that this is true “up to a logarithmic factor.”

In this paper we show that mixed nite element methods for a fairly general second order elliptic problem with variable coeecients can be given a non-mixed formulation. (Lower order terms are treated, so our results apply also to parabolic equations.) We deene an approximation method by incorporating some projection operators within a standard Galerkin method, which we call a projection nite ele...

In this paper we show that mixed nite element methods for a fairly general second order elliptic problem with variable coeecients can be given a non-mixed formulation. (Lower order terms are treated, so our results apply also to parabolic equations.) We deene an approximation method by incorporating some projection operators within a standard Galerkin method, which we call a projection nite ele...

We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n − 1)dimensional projection being given. We give a number of examples, like a four-dimensional body of constant width whose 3D-projection is the classical Meissner’s body.