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A Casorati-Weierstrass theorem for holomorphic maps and invariant $$\sigma$$-fields of homomorphic diffusions. (English) Zbl 0967.58019
The author improves the Casorati-Weierstrass theorem for holomorphic maps from some general manifolds to complex projective space. In fact the following interesting theorem is proved: No nonconstant holomorphic maps from a Kähler manifold which cannot admit nonconstant bounded harmonic functions to a complex projective space omit hyperplanes of positive measure.

##### MSC:
 58J65 Diffusion processes and stochastic analysis on manifolds 60J60 Diffusion processes
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