Non-univalent harmonic maps homotopic to diffeomorphisms.
This paper answers, by the negative, a question of S.T. Yau, by showing that a harmonic map homotopic to a diffeomorphism between negatively curved compact manifolds is not necessarily univalent (i.e. one-to-one or injective). \newline This is achieved by constructing, in any dimension at least six, a pair of purpose-built closed connected negatively curved manifolds, together with a diffeomorphism, which, by Eells-Sampson's theorem, admits a unique homotopic harmonic map, shown to be non-univalent. The construction of these manifolds is based on the intricate building of an arithmetic group and the corresponding quotient manifolds.
scientific article; zbMATH DE number 1782640