Ricci flow on 3-manifolds with symmetry
Name
50594786-MIT.pdf
Description
Full printable version
Size
2.83 MB
Format
Adobe PDF
Checksum (MD5)
074ff1543cb4b067bf09a2a925b8b1fd
Author(s)
Cao, Xiaodong, 1972-
Advisor(s)
Gang Tian.
Date Issued
2002
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, we proved that for a 3-manifold S2 x S1 with warped product metric, the isoperimetric ratio on the base manifold S2 has a low positive bound away from zero, if the scalar curvature on the 3-manifold is positive. We also obtained a monotonicity result under the condition that the length of the optimal curve for isoperimetric ratio shrinks to zero under Ricci flow. This result excludes the product of a cigar soliton [Sigma]² with R¹ as the dilation limit of the Ricci flow equation. We also obtained an inequality of the curvature ratio Rmin/Rmax on the dilation limit for compact 3-manifold with positive scalar curvature.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.
Includes bibliographical references (p. 51-53).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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