  S. Lang conjectured in 1974 that a hyperbolic algebraic variety defined over
a number field has only finitely many rational points, and its analogue over
function fields. We discuss the Nevanlinna-Cartan theory over function fields
of arbitrary dimension and apply it for Diophantine property of hyperbolic
projective hypersurfaces (homogeneous Diophantine equations) constructed by
Masuda-Noguchi. We also deal with the finiteness property of $S$-units points
of those Diophantine equations over number fields.
