Resumen de Maximal and linearly inextensible polynomials

J. Borcea

• Let S(n,0) be the set of monic complex polynomials of degree n≥2 having all their zeros in the closed unit disk and vanishing at 0. For p∈S(n,0) denote by |p|0 the distance from the origin to the zero set of p′. We determine all 0-maximal polynomials of degree n, that is, all polynomials p∈S(n,0) such that |p|0≥|q|0 for any q∈S(n,0). Using a second order variational method we then show that although some of these polynomials are linearly inextensible, they are not locally maximal for Sendov's conjecture.