[2] He is a fellow of the American Mathematical Society since 2018, for "contributions to differential geometry, particularly minimal surface theory, and for pioneering the use of computer graphics as an aid to research.
[6] One year later, Hoffman and Joel Spruck extended Michael and Simon's work to the setting of functions on immersed submanifolds of Riemannian manifolds.
Hoffman and William Meeks proved that any minimal surface which is contained in a half-space must fail to be properly immersed.
The proof is a simple application of the maximum principle and unique continuation for minimal surfaces, based on comparison with a family of catenoids.
This enhances a result of Meeks, Leon Simon, and Shing-Tung Yau, which states that any two complete and properly immersed minimal surfaces in three-dimensional Euclidean space, if both are nonplanar, either have a point of intersection or are separated from each other by a plane.