Ricci flow on 3-manifolds with symmetry
Author(s)Cao, Xiaodong, 1972-
Massachusetts Institute of Technology. Dept. of Mathematics.
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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.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.Includes bibliographical references (p. 51-53).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.; Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology