Tunneling for the $\overline{\partial }$-operator

Johannes Sjöstrand, Martin Vogel

We study the small singular values of the $2$-dimensional semiclassical differential operator $P=2{\mathrm{e}}^{-\varphi /h}\circ h{D}_{\overline{z}}\circ {\mathrm{e}}^{\varphi /h}$ on $S^1+i{S}^1$…