Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/121121
Title: SYMMETRIC EXISTENCE RESULTS, AND AGGREGATED, TOWERING BLOW-UP SEQUENCES FOR THE PRESCRIBED SCALAR CURVATURE EQUATION ON SN
Authors: ZHOU FENG
Keywords: Scalar Curvature, Blow-up, Flow Equation, Critical Points
Issue Date: 31-Mar-2015
Source: ZHOU FENG (2015-03-31). SYMMETRIC EXISTENCE RESULTS, AND AGGREGATED, TOWERING BLOW-UP SEQUENCES FOR THE PRESCRIBED SCALAR CURVATURE EQUATION ON SN. ScholarBank@NUS Repository.
Abstract: This thesis consists of two parts on the prescribed scalar curvature equation on the standard sphere Sn. In the first part, we use the negative gradient flow equation for the prescribed scalar curvature equation to obtain existence theorems in cases where the prescribed function K exhibits reflection or rotation symmetry. We also demonstrate that the "one bubble" condition cannot be totally taken away. In the second part, by using annular domains, we obtain constructive results on blow-up sequences of infinite number of solutions for the prescribed (and fixed) scalar curvature equation on Sn (n>=6), including aggregated and towering blow-ups. The constructions make use of the Lyapunov-Schmidt reduction method, count on the hyperbolic structure on the collection of standard bubbles, and apply a degree theory for the quasi-hyperbolic gradient.
URI: http://scholarbank.nus.edu.sg/handle/10635/121121
Appears in Collections:Ph.D Theses (Open)

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