442 research outputs found
Monotonicity Formulae and Holomorphicity of Harmonic Maps between K\"ahler manifolds
In this paper, we introduce the stress-energy tensors of the partial energies
E'(f) and E"(f) of maps between Kaehler manifolds. Assuming the domain
manifolds poss some special exhaustion functions, we use these stress-energy
tensors to establish some monotonicity formulae of the partial energies of
pluriharmonic maps into any Kaehler manifolds and harmonic maps into Kaehler
manifolds with strongly semi-negative curvature respectively. These
monotonicity inequalities enable us to derive some holomorphicity and Liouville
type results for these pluriharmonic maps and harmonic maps. We also use the
stress-energy tensors to investigate the holomorphic extension problem of CR
maps.Comment: 46 page
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