  We study the brane world scenario of a single brane (or a single stack of
branes) with codimension higher than one. When the extra dimensions are not
small, localization of gravity around the brane is needed in order to reproduce
the observable four-dimensional gravity. We focus on the case of noncompact
extra dimensions, where the possibility of localized gravity becomes
non-trivial. We show that in large class of gravity models, localization of
massless gravity is not possible for codimension-2 branes with at least one
noncompact extra dimension. With additional mild assumptions on field
backgrounds, we also show that it is not possible for higher codimensional
branes with two or more noncompact extra dimensions.
