Continuous leafwise harmonic functions on codimension one transversely isometric foliations

Abstract

Let ℱ be a codimension one foliation on a closed manifold ℳ which admits a transverse dimension one Riemannian foliation. Then any continuous leafwise harmonic functions are shown to be constant on leaves.

Keywords

• Codimension one foliations
• leafwise harmonic functions
• stationary measures