Harnack–Thom inequalities for mappings of real algebraic varieties

Several analogues of the Harnack and Thom inequalities are proved for mappings of real algebraic varieties. In the statement of the analogues of the Thom inequalities an essential role is played by the notion of $GM$-variety introduced in the paper; in this connection the question of characterizing the $GM$-varieties among all real algebraic varieties is also considered.
Bibliography: 6 titles.