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Construction of blow-up sequences for the prescribed scalar curvature equation on \(S^n\). III. Aggregated and towering blow-ups

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Abstract

Using annular domains introduced in Part II (Leung, Calc Var PDE 46:1–29, 2013), we present constructive results on blow-up sequences of infinite number of solutions for the (prescribed and fixed) conformal scalar curvature equation on \(S^n\) (\(n\ge 6\)), including aggregated and towering blow-ups. The constructions make use of the Lyapunov–Schmidt reduction method, and count on the hyperbolic structure on the collection of standard bubbles.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 10, Lower Kent Ridge Road, Singapore, 119076, Republic of Singapore

    Man Chun Leung & Feng Zhou

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  1. Man Chun Leung
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  2. Feng Zhou
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Correspondence to Man Chun Leung.

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Communicated by A. Malchiodi.

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Leung, M.C., Zhou, F. Construction of blow-up sequences for the prescribed scalar curvature equation on \(S^n\). III. Aggregated and towering blow-ups. Calc. Var. 54, 3009–3035 (2015). https://doi.org/10.1007/s00526-015-0892-4

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  • DOI: https://doi.org/10.1007/s00526-015-0892-4

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