Report on Harmonic Functions of Polynomial Growth on Riemannian Manifolds
碩士 === 國立中正大學 === 應用數學研究所 === 90 === In this report, we study the harmonic functions of polynomial growth on Riemannian manifolds, especially focus on estimate of the dimension of such spaces on complete Riemannian manifolds with non-negative Ricci curvature. This subject began in 1975, w...
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| Format: | Others |
| Language: | en_US |
| Published: |
2002
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| Online Access: | http://ndltd.ncl.edu.tw/handle/89311712294203491062 |
| Summary: | 碩士 === 國立中正大學 === 應用數學研究所 === 90 === In this report, we study the harmonic functions of polynomial growth on Riemannian manifolds, especially focus on estimate of the dimension of such spaces on complete Riemannian manifolds with non-negative Ricci curvature. This subject began in 1975, when S. T. Yau proved the strong Liouville property on complete manifolds with non-negative Ricci curvature. Yau conjectured that the space of harmonic functions of polynomial growth on Riemannian manifolds with non-negative Ricci curvature is finite dimensional. In a series of paper, Colding and Minicozzi proved and went beyond Yau's conjecture. P. Li and J. P. Wang proved further results on this topic afterwards.
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