Monotonicity formulae and holomorphicity of harmonic maps between Kähler manifolds (Q2872024)

In this paper, the author introduces the stress-energy tensors of the partial energies \(E'(f)\) and \(E''(f)\) of maps between Kähler manifolds. Assuming the domain manifolds possess some special exhaustion functions, the author employs the energy tensors to establish certain monotonicity formulae of partial energies of pluriharmonic maps into any Kähler manifolds and of harmonic maps into Kähler manifolds with strongly semi-negative curvature. The monotonicity inequalities enable the author to derive some holomorphicity and Liouville-type results for such mappings. The stress-energy tensors are also used to investigate the holomorphicity extension problem of Cauchy-Riemann maps.