  Kirigami, an ancient paper cutting art, offers a promising strategy for
2D-to-3D shape morphing through cut-guided deformation. Existing kirigami
designs for target 3D curved shapes rely on intricate cut patterns in thin
sheets, making the inverse design challenging. Motivated by the Gauss-Bonnet
theorem that correlates the geodesic curvature along the boundary with the
topological Gaussian curvature, here, we exploit programming the curvature of
cut boundaries rather than complex cut patterns in kirigami sheets for target
3D curved topologies through both forward and inverse designs. Such a new
strategy largely simplifies the inverse design. We demonstrate the achievement
of varieties of dynamic 3D shape shifting under both mechanical stretching and
remote magnetic actuation, and its potential application as an untethered
predator-like kirigami soft robot. This study opens a new avenue to encode
boundary curvatures for shape-programing materials with potential applications
in shape-morphing structures, soft robots, and multifunctional devices.
