Conformal Laplacian and Conical Singularities

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 ${Ł}_{g}u=Q{u}^{\alpha }$ with $1\le \alpha \le \frac{n+2}{n-2}$ near each singular point. In particular, we derive the asymptotic of the Yamabe metric near such singularity.

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