Monotonicity Formulae and Holomorphicity of Harmonic Maps between Kähler manifolds

Details Monotonicity Formulae and Holomorphicity of Harmonic Maps between Kähler manifolds Monotonicity Formulae and Holomorphicity of Harmonic Maps between Kähler manifolds

2010-11-28

arxiv.org/abs/1011.6016v2

Mathematics

Differential Geometry

46 pages

Scientific paper

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.

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