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Conformal Laplacian and Conical Singularities

Boris Botvinnik·Serge Preston
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Abstract

We study a behavior of the conformal Laplacian operator $Ł_g$ on a manifold with \emph{tame conical singularities}: when each singularity is given as a cone over a product of the standard spheres. We study the spectral properties of the operator $Ł_g$ on such manifolds. We describe the asymptotic of a general solution of the equation $Ł_g u = Q u^α$ with $1\leq α\leq \frac{n+2}{n-2}$ near each singular point. In particular, we derive the asymptotic of the Yamabe metric near such singularity.

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Boris Botvinnik, Serge Preston. 2002-12-10. Conformal Laplacian and Conical Singularities. https://arxiv.org/abs/math/0201058

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