 ![Left: Geometry of a complex domain, with a bottleneck (in the lower part), two inner blocked points, and an inward crack (on the right upper side). The question is: is there localization in this structure, which modes will be localized and where? Center and right: 0D representations of the landscape $u$ for the Laplacian (center) and the bi-Laplacian (right) in the same domain. The colors correspond to the height of the landscape. The (thin black) streamlines help to detect the valley lines, which are then highlighted as thick red curves. These valleys delimit 0 subregions of localization for the Laplacian and 0 subregions for the bi-Laplacian.[]{data-label="fig:cplate_u"}](cplate_