Abstract.
The main purpose of this article is to generalize a theorem about the size of minimal submanifolds in Euclidean spaces. In fact, we state and prove a non-existence theorem about harmonic maps from a stochastically complete manifold into a cone type domain. The proof is based on a generalized version of the maximum principle applied to the Lapalace-Beltrami operator on Riemannian manifolds.
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Received: 2 August 2007, Revised: 14 April 2008
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Ranjbar-Motlagh, A. On harmonic maps from stochastically complete manifolds. Arch. Math. 92, 637–644 (2009). https://doi.org/10.1007/s00013-009-2539-1
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DOI: https://doi.org/10.1007/s00013-009-2539-1