Although the existence and uniqueness of Strebel differentials are proved by Jenkins and Strebel,the specific constructions of Strebel differentials are difficult.Two special kinds of special Strebel differentials are constructed in [5,6].The Strebel rays [3] and the eventually distance minimizing rays [9] are important in Teichmüller spaces and moduli spaces,respectively.Motivated by the study of [3,9],two special kinds of Strebel rays in the real hyper-elliptic subspace of Teichmüller space and two special kinds of EDM rays in the real hyper-elliptic subspace of moduli space are studied in this article.
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