Report on Geometiy at Infinity and Volume Comparison Theorem
碩士 === 國立中正大學 === 應用數學研究所 === 90 === The volume comparison theory plays an important role in differential geometry. In this report, first we shall give a brief survey on results related to the volume growth condition. In particular, there are many interesting and significant re...
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| Format: | Others |
| Language: | en_US |
| Published: |
2002
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| Online Access: | http://ndltd.ncl.edu.tw/handle/98574585111787668987 |
| Summary: | 碩士 === 國立中正大學 === 應用數學研究所 === 90 === The volume comparison theory plays an important role in differential geometry. In this report, first we shall give a brief survey on results related to the volume growth
condition. In particular, there are many interesting and significant results on finite topological type under the assumption of maximal volume growth with appropriate curvature conditons. Secondly, we shall study the geometric behavior of complete, noncompact Riemannian manifolds at infinity. The common tool is comparison theorem.
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