  For a convex domain K in the complex plane C, the well-known general Markov
inequality asserting that a polynomial p of degree n ||p'|| < c(K) n^2 ||p||
holds. On the other hand for polynomials in general, ||p'|| can be arbitrarily
small as compared to ||p||.
  The situation changes when we assume that the polynomials have all their
zeroes in the convex body K. This problem of lower bound for Markov factors was
first investigated by Tur\'an in 1939. Tur\'an showed ||p'|| \ge n/2 ||p|| for
the unit disk D and ||p'|| > c \sqrt{n} ||p|| for the unit interval I:=[-1,1].
Soon after that, J. Er\H od published a long article, discussing various
extensions of the results and methods of Tur\'an.
  For decades, Er\H od's paper was quoted only for the explicit calculation of
the exact constant of the interval case. However, in recent years Levenberg and
Poletsky, Erd\'elyi and also the author investigated Tur\'an's problem for
various sets - basically, convex domains. In this context the much richer
content of Er\H od's work is to be realized again.
  Thus, the aim of the paper is twofold. On the one hand we give an account of
the half-forgotten, old Hungarian article of Er\H od, also commemorating its
author. On the other hand we report on recent developments with particular
emphasis on development of one of the key observations of Er\H od, namely, the
role of the curvature of the boundary curve in the estimation of the lower
bound of Markov factors.
