Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/37879
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dc.titleOn the locally conformally flat hyper-surfaces with nonnegative scalar curvature in R^5
dc.contributor.authorZHOU JIURU
dc.date.accessioned2013-05-31T18:02:01Z
dc.date.available2013-05-31T18:02:01Z
dc.date.issued2013-01-11
dc.identifier.citationZHOU JIURU (2013-01-11). On the locally conformally flat hyper-surfaces with nonnegative scalar curvature in R^5. ScholarBank@NUS Repository.
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/37879
dc.description.abstractThis thesis studies the geometry and topology of manifolds from an extrinsic point of view. Suppose M^4 is a complete non-compact locally conformally flat hyper-surface with non-negative scalar curvature immersed in R^5. Given some conditions on the second fundamental form and the mean curvature, we should show that if the L^4 norm of the mean curvature of M is bounded by some constant which does not depend on the manifold M, then M is embedded in R^5. This result should be a generalization of S. M uller and V. Sver ak's result on two dimensional manifolds which immersed in R^n.
dc.language.isoen
dc.subjectMean curvature, Second fundamental form, Immersion, Embedding
dc.typeThesis
dc.contributor.departmentMATHEMATICS
dc.contributor.supervisorXU XINGWANG
dc.description.degreePh.D
dc.description.degreeconferredDOCTOR OF PHILOSOPHY
dc.identifier.isiutNOT_IN_WOS
Appears in Collections:Ph.D Theses (Open)

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