Characterization of continuity of Siciak-Zaharjuta extremal functions on compact Hermitian manifolds

Abstract: For a compact subset in a compact Hermitian manifold, we prove that the continuity of the extremal function at a given point in the set is a local property and that the continuity of a weighted extremal function follows from the continuities of the extremal function and the weight function. These results are generalizations of the results of Nguyen \cite{Ng24} on compact Kähler manifolds. Moreover, for a compact subset in a compact Hermitian manifold, we characterize the continuity of the extremal function via the local (L)-regularity, which is equivalent to the weak local (L)-regularity.