A Banach space is polyhedral if the unit ball of each of its finite dimensional subspaces is a polyhedron. It is known that a polyhedral Banach space has a separable dual and is c0-saturated, i.e., each closed infinite dimensional subspace contains an isomorph of c0. In this paper, we show that the Orlicz sequence space hM is isomorphic to a polyhedral Banach space if limt→0 M(Kt)/M(t) = ∞ for ...

We prove a vanishing theorem for the Hodge number h 2;1 of projective toric varieties provided by a certain class of polytopes. We explain how this Hodge number also gives information about the deformation theory of the toric Gorenstein singularity derived from the same polytope. In particular, the vanishing theorem for h 2;1 implies that these deformations are unobstructed.

We introduce a new combinatorial abstraction for the graphs of polyhedra. The new abstraction is a flexible framework defined by combinatorial properties, with each collection of properties taken providing a variant for studying the diameters of polyhedral graphs. One particular variant has a diameter which satisfies the best known upper bound on the diameters of polyhedra. Another variant has ...

We study the problem of when the collection of the recession cones of a polyhedral complex forms also a complex. We exhibit an example showing that this is no always the case. We also show that if the support of the given polyhedral complex satisfies a Minkowski-Weyl type condition, then the answer is positive. As a consequence, we obtain a classification theorem for proper toric schemes over a...

Abstract. We derive pointwise a posteriori residual-based error estimates for finite element solutions to the Stokes equations in polyhedral domains. The estimates relies on the regularity of the of Stokes equations and provide an upper bound for the pointwise error in the velocity field on polyhedral domains. Whereas the estimates provide upper bounds for the pointwise error in the gradient of...