About semiboundness of $\delta$-perturbations of the Laplacian supported by curves with angle points

Еlementary self-adjoint perturbations of the Laplacian supported by curves with singular angle points are studied in $\mathbb R^3$ and $\mathbb R^4$. The perturbations are shown to be semibounded in $\mathbb R^3$ and unsemibounded in $\mathbb R^4$. In the last case semiboundness may take place in subspaces of a given symmetry as it is shown in simple example.