  We present a first procedure that can estimate -- with statistical
consistency guarantees -- any local-maxima of a density, under benign
distributional conditions. The procedure estimates all such local maxima, or
$\textit{modal-sets}$, of any bounded shape or dimension, including usual
point-modes. In practice, modal-sets can arise as dense low-dimensional
structures in noisy data, and more generally serve to better model the rich
variety of locally-high-density structures in data.
  The procedure is then shown to be competitive on clustering applications, and
moreover is quite stable to a wide range of settings of its tuning parameter.
