In a recent paper, the authors have proved results characterizing convexity-preserving maps deened on a subset of a not-necessarily nite dimensional real vector space as projective maps. The purpose of this note is threefold. First, we state a theorem characterizing continuous, injective, convexity-preserving maps from a relatively open, connected subset of an aane subspace of R m into R n as p...

We study convexity properties of the zeros of some special functions that follow from the convexity theorem of Sturm. We prove results on the intervals of convexity for the zeros of Laguerre, Jacobi and ultraspherical polynomials, as well as functions related to them, using transformations under which the zeros remain unchanged. We give upper as well as lower bounds for the distance between con...

Recently Kamiyama, Katoh, and Takizawa have shown a theorem on packing arc-disjoint arborescences that is a proper extension of Edmonds’ theorem on disjoint spanning branchings. We show a further extension of their theorem, which makes clear an essential rôle of a reachability condition played in the theorem. The right concept required for the further extension is “convexity” instead of “reacha...

We show that the image cone of a moment map for an action of a torus on a contact compact connected manifold is a convex polyhedral cone and that the moment map has connected fibers provided the dimension of the torus is bigger than 2 and that no orbit is tangent to the contact distribution. This may be considered as a version of the Atiyah Guillemin Sternberg convexity theorem for torus action...

We extend the Bipolar Theorem of Brannath and Schachermayer (1999) to the space of nonnegative càdlàg supermartingales on a filtered probability space. We formulate the notion of fork-convexity as an analogue to convexity in this setting. As an intermediate step in the proof of our main result we establish a conditional version of the Bipolar theorem. In an application to mathematical finance w...

In this paper we provide sufficient conditions that ensure the convexity of the inverse images of an operator, monotone in some sense. Further, conditions that ensure the monotonicity, respectively the local injectivity of an operator are also obtained. Combining the conditions that provide the local injectivity, respectively the convexity of the inverse images of an operator, we are able to ob...