Conformal Laplacian and Conical Singularities

Details Conformal Laplacian and Conical Singularities Conformal Laplacian and Conical Singularities

2002-01-08

arxiv.org/abs/math/0201058v3

Mathematics

Differential Geometry

Revision 61 pages

Scientific paper

We study a behavior of the conformal Laplacian operator $\L_g$ 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 $\L_g$ on such manifolds. We describe the asymptotic of a general solution of the equation $\L_g u = Q u^{\alpha}$ with $1\leq \alpha\leq \frac{n+2}{n-2}$ near each singular point. In particular, we derive the asymptotic of the Yamabe metric near such singularity.

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