Towering Phenomena for the Yamabe Equation on Symmetric Manifolds

Let (M, g) be a compact smooth connected Riemannian manifold (without boundary) of dimension N ae<yen> 7. Assume M is symmetric with respect to a point xi (0) with non-vanishing Weyl's tensor. We consider the linear perturbation of the Yamabe problem We prove that for any k a a"center dot, there exists epsilon (k) > 0 such that for all epsilon a (0, epsilon (k) ) the problem (P (oee-) ) has a symmetric solution u (epsilon) , which looks like the superposition of k positive bubbles centered at the point xi (0) as epsilon -> 0. In particular, xi (0) is a towering blow-up point.
Publisher
SPRINGER
Issue Date
2017-07
Language
English
Keywords

CONFORMALLY FLAT MANIFOLDS; CRITICAL SOBOLEV EXPONENT; NONLINEAR ELLIPTIC-EQUATIONS; SCALAR CURVATURE; RIEMANNIAN-MANIFOLDS; COMPACTNESS; PROOF

Citation

POTENTIAL ANALYSIS, v.47, no.1, pp.53 - 102

ISSN
0926-2601
DOI
10.1007/s11118-016-9608-4
URI
http://hdl.handle.net/10203/225092
Appears in Collection
MA-Journal Papers(저널논문)
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