A Theorem of Liouville Type for Harmonic Morphisms
β Scribed by Gundon Choi; Gabjin Yun
- Book ID
- 110289251
- Publisher
- Springer
- Year
- 2001
- Tongue
- English
- Weight
- 57 KB
- Volume
- 84
- Category
- Article
- ISSN
- 0046-5755
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We give a very simple function theoretic proof to a Liouville type theorem for harmonic functions defined on exterior domains obtained and proved in a convexity theoretic method by F. Cammaroto and A. ChinnΔ±. The theorem itself is also slightly generalized.
Let N be a compact Riemannian manifold. A self-similar solution for the heat flow is a harmonic map from (R n , e -|x| 2 /2(n-2) ds 2 0 ) to N (n β₯ 3), which was also called a quasiharmonic sphere (cf. Lin and Wang (1999) [1]). (Here ds 2 0 is the Euclidean metric in R n .) It arises from the blow-