Abstract
We prove that if a given complete Riemarmian manifold is roughly isometric to a complete Riemarmian manifold satisfying the volume doubling condition, the Poincare inequality and the finite covering condition at infinity on each end, then every positive harmonic function on the manifold is asymptotically constant at infinity on each end. This result is a direct generalization of those of Yau and of Li and Tam.
| Original language | English |
|---|---|
| Pages (from-to) | 73-95 |
| Number of pages | 23 |
| Journal | Journal of the Korean Mathematical Society |
| Volume | 36 |
| Issue number | 1 |
| State | Published - 1999 |
Keywords
- Asymptotically constant
- Capacity
- End
- Finite covering
- Harmonic function
- Harmonic map
- Harnack inequality
- Liouville theorem
- Parabolicity
- Poincaréinequality
- Rough isometry
- Sobolev's inequality
- Volume doubling