Analysis of the Laplacian of an incomplete manifold with almost polar boundary

Abstract

Motivated by recent interest in global analysis of singular manifolds, we establish the essential self-adjointness of a Laplacian, a Liouville property of subharmonic functions, conservativeness and parabolicity of an incomplete manifold. These results are applicable for manifolds with fractal Cauchy boundary.

Keywords

• laplacian
• essential self-adjointness
• lioville property
• conservativeness
• parabolicity
• incomplete manifold
• singular manifold