We characterize the open sets in the sphere that are geodesically convex in any containing domain with respect to various conformal metrics.

We show that a PL-realization of a closed connected manifold of dimension n − 1 in R (n ≥ 3) is the boundary of a convex polyhedron if and only if the interior of each (n− 3)-face has a point, which has a neighborhood lying on the boundary of a convex n-dimensional body. This result is derived from a generalization of Van Heijenoort’s theorem on locally convex manifolds to the spherical case. N...

The Brunn Minkowski theory of convex bodies and mixed volumes has provided many tools for solving problems involving projections and valuations of compact convex sets in Euclidean space. Among the most beautiful results of twentieth century convexity is Hadwiger's characterization theorem for the elementary mixed volumes (Quermassintegrals); (see [3, 5, 9]). Hadwiger's characterization leads to...

Abstract By the first welfare theorem, competitive market equilibria belong to core and hence are Pareto optimal . Letting money be a commodity, this paper turns these two inclusions around. More precisely, by generalizing second theorem we show that said solutions may coincide as common fixed point for one same system. Mathematical arguments invoke conjugation, convolution, generalized gradien...

Let Ω be a bounded C∞-smoothly bounded domain in C. For such a domain we define a new notion between strict pseudo-convexity and pseudo-convexity: the size of the set W of weakly pseudo-convex points on ∂Ω is small with respect to Minkowski dimension: near each point in the boundary ∂Ω, there is at least one complex tangent direction in which the slices of W has a upper Minkowski dimension stri...

In [26], Olofsson introduced a kind of second order homogeneous partial differential equation. We call the solution this equation real kernel ?-harmonic mappings. paper, we study some geometric properties give univalence criteria and sufficient coefficient conditions for mappings that are fully starlike or convex ?, ? [0, 1). Furthermore, establish Landau type theorem

We study the relations between boundaries for algebras of holomorphic functions on Banach spaces and complex convexity of their balls. In addition, we show that the Shilov boundary for algebras of holomorphic functions on an order continuous sequence space X is the unit sphere SX if X is locally c-convex. In particular, it is shown that the unit sphere of the OrliczLorentz sequence space λφ,w i...

We give some remarks on geodesics in the space of Kähler metrics that are defined for all time. Such curves conjecturally induced by holomorphic vector fields, and we show this is indeed so regular geodesics, whereas question generalized still open (as far as know). also a result about derivative such which implies variant theorem Atiyah Guillemin-Sternberg convexity image certain moment maps.

By making use of the concept basic (or q-) calculus, many subclasses analytic and symmetric q-starlike functions have been defined studied from different viewpoints perspectives. In this article, we introduce a new class meromorphic multivalent close-to-convex with help q-differential operator. Furthermore, investigate some useful properties such as sufficiency criteria, coefficient estimates, ...