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Denjoy-Ahlfors Theorem for Harmonic Func...
Miklyukov, Vladimir ...

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Denjoy-Ahlfors Theorem for Harmonic Functions on Riemannian Manifolds and External Structure of Minimal Surfaces by Miklyukov, Vladimir M. ( Author )
Lemonjar Open Access
N.A
13-03-2009
We extend the well-known Denjoy-Ahlfors theorem on the number of different asymptotic tracts of holomorphic functions to subharmonic functions on arbitrary Riemannian manifolds. We obtain some new versions of the Liouville theorem for $\p$-harmonic functions without requiring the geodesic completeness requirement of a manifold. Moreover, an upper estimate of the topological index of the height function on a minimal surface in $\R{n}$ has been established and, as a consequence, a new proof of Bernstein's theorem on entire solutions has been derived. Other applications to minimal surfaces are also discussed.
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English
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MYR 0.00
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https://arxiv.org/abs/0903.2326
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