We introduce a connection between Newhouse thickness and patterns through variant of Schmidt’s game introduced by Broderick, Fishman Simmons. This yields an explicit, robust checkable condition that ensures Cantor set in the real line contains long arithmetic progressions and, more generally, homothetic copies large finite sets.

This article describes a new proof of the equality condition for the Brunn-Minkowski inequality. The Brunn-Minkowski Theorem asserts that, for compact convex sets K,L ⊆ Rn, the n-th root of the Euclidean volume Vn is concave with respect to Minkowski combinations; that is, for λ ∈ [0, 1], Vn((1− λ)K + λL) ≥ (1− λ)Vn(K) + λVn(L). The equality condition asserts that if K and L both have positive ...

A selfsimilar manifold is a Riemannian (M,g) endowed with homothetic vector field ξ. We characterize global manifolds and describe the structure of local manifolds. prove that any potential conical or Euclidean space. radiant Hessian (M,∇,g,ξ) such ∇ξ=λId, where λ constant. locally isomorphic to product

In this paper, we study the curvature of a semi-Riemannian manifold M̃ of quasi-constant curvature admits some half lightlike submanifolds M . The main result is two characterization theorems for M̃ admits extended screen homothetic and statical half lightlike submanifolds M such that the curvature vector field of M̃ is tangent to M .

Two components of spherically symmetric, inhomogeneous dust penetrating each other are introduced as a generalization of the well–known Tolman–Bondi dust solution. The field equations of this model are formulated and general properties are discussed. Special solutions with additional symmetries — an extra Killing– or homothetic vector — and their matching to the corresponding Tolman–Bondi solut...

In 1957, H. Hadwiger conjectured that a convex body K in a Euclidean d-space, d 1, can always be covered by 2 smaller homothetic copies of K. We verify this conjecture when K is the polar of a cyclic d-polytope. Mathematics Subject Classifications (1991): 52A15, 52A20.

We analyze a macroeconomic model of monopolistic competition in which consumers earn unequal incomes. When preferences are non-homothetic, the distribution of income affects equilibrium mark-ups and equilibrium product diversity. Inequality, Market Power, and Product Diversity Reto Foellmi, University of Zurich Josef Zweimüller, University of Zurich, CESifo, IZA, and CEPR∗†

For convex partitions of a convex body B we prove that we can put a homothetic copy of B into each set of the partition so that the sum of homothety coefficients is ≥ 1. In the plane the partition may be arbitrary, while in higher dimensions we need certain restrictions on the partition.

To determine whether an industry exhibits constant returns to scale, whether the production fUnction is homothetic, or whether inputs are separabl~ a common approach is to specify a cost function, estimate its parameters using data such as prices and quantities of inputs, and then test the parametric restrictions corresponding to constant returns, a homothetic technology, or separability. Stati...

In the present paper, we study quasi-Yamabe solitons and almost on lightlike hypersurfaces of semi-Riemannian manifolds endowed with a torse-forming vector field. We show some conditions for to be quasi- Yamabe tangential component field as soliton particular, also specify (n + 2)-dimension constant curvature solitons. Besides, provide geometric properties satisfying solitons, gradient Furtherm...