Multiple Field Ultra Slow Roll Inflation: Primordial Black Holes From
  Straight Bulk And Distorted Boundary
  We study a model of two-field ultra-slow-roll (USR) inflation bounded by a
curve in the field space. Curvature perturbations and non-Gaussianities can be
enhanced both during the USR phase and from the inhomogeneities at the
boundary. We employ the full non-linear $\delta N$ formalism to calculate the
probability distribution function (PDF) for curvature perturbation
non-perturbatively and show that the non-linear effects can significantly
enhance the abundance of the primordial black holes (PBHs). For large curvature
perturbations, the PDF has a universal exponential tail, but for the
intermediate values, the PDF -- and, therefore, the abundance of the PBHs --
depend sensitively on the geometry of the boundary.
