[4] Shi is well-known for his foundational work with Luen-Fai Tam on compact and smooth Riemannian manifolds-with-boundary whose scalar curvature is nonnegative and whose boundary is mean-convex.
This is particularly simple in three dimensions, where every manifold has a spin structure and a result of Louis Nirenberg shows that any positively-curved Riemannian metric on the two-dimensional sphere can be isometrically embedded in three-dimensional Euclidean space in a geometrically unique way.
Shi and Tam's proof adopts a method, due to Robert Bartnik, of using parabolic partial differential equations to construct noncompact Riemannian manifolds-with-boundary of nonnegative scalar curvature and prescribed boundary behavior.
By combining Bartnik's construction with the given compact manifold-with-boundary, one obtains a complete Riemannian manifold which is non-differentiable along a closed and smooth hypersurface.
From the perspective of research literature in general relativity, Shi and Tam's result is notable in proving, in certain contexts, the nonnegativity of the Brown-York quasilocal energy of J. David Brown and James W.