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Trapped modes, that is, localized unforced oscillations of fluid in presence of floating structures and bottom topography, have been a topic of considerable interest over many years and substantial effort has been put, for a variety of different geometries, into finding the solutions and conditions of their existence or absence. However, the class of geometries having cusp points has been avoided ...

On the Non-Existence of Surface Waves Trapped by Submerged Obstructions Having Exterior Cusp Points