Harmonic functions on R-covered foliations
نویسندگان
چکیده
Let (M,F) be a compact codimension one foliated manifold whose leaves are endowed with Riemannian metrics and consider continuous functions on M that are harmonic along the leaves of F . If every such function is constant on leaves we say that (M,F) has the Liouville property. Our main result is that codimension-one foliated bundles over compact negatively curved manifolds satisfy the Liouville property. A related result for R-covered foliations is also established.
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Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of F . If every such function is constant on leaves we say that (M,F) has the Liouville property. Our main result is that codimension-one foliated bundles over compact negatively curved manifolds satisfy the Liouvil...
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