SuJicient conditions are given under which convex combinations of stable (complex and real) polynomials are stable.

Given a collection of minimal graphs,M1,M2, . . . ,Mn, with isothermal parametrizations in terms of the Gauss map and height differential, we give sufficient conditions onM1,M2, . . . ,Mn so that a convex combination of themwill be a minimal graph. We will then provide two examples, taking a convex combination of Scherk’s doubly periodic surface with the catenoid and Enneper’s surface, respecti...

This is a continuation of [6]. In this article, we proved that convex combination on convex family is convex. and [9] provide the notation and terminology for this paper. 1. CONVEX COMBINATIONS ON CONVEX FAMILY The following propositions are true: (1) For every non empty RLS structure V and for all convex subsets M, N of V holds M ∩ N is convex. (2) Let V be a real unitary space-like non empty ...