Eigenvalues for a Schr\"odinger operator on a closed Riemannian manifold with holes

Olivier Lablee

Abstract


In this article we consider a closed Riemannian manifold $(M,g)$
and $A$ a subset of $M$. The purpose of this article is the comparison
between the eigenvalues $\left(\lambda_{k}(M)\right)_{k\geq1}$ of
a Schr\"odinger operator $P:=-\Delta_{g}+V$ on the manifold $(M,g)$
and the eigenvalues $\left(\lambda_{k}(M-A)\right)_{k\geq1}$ of $P$
on the manifold $(M-A,g)$ with Dirichlet boundary conditions.

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