Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/37879
Title: On the locally conformally flat hyper-surfaces with nonnegative scalar curvature in R^5
Authors: ZHOU JIURU
Keywords: Mean curvature, Second fundamental form, Immersion, Embedding
Issue Date: 11-Jan-2013
Source: ZHOU JIURU (2013-01-11). On the locally conformally flat hyper-surfaces with nonnegative scalar curvature in R^5. ScholarBank@NUS Repository.
Abstract: This 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.
URI: http://scholarbank.nus.edu.sg/handle/10635/37879
Appears in Collections:Ph.D Theses (Open)

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