In addition to his teaching and research duties, Minicozzi serves as an editor of the American Journal of Mathematics.
He gave an invited address on this work at the 2006 ICM in Madrid, a London Mathematical Society Spitalfields Lecture in 2007, the thirty-fifth University of Arkansas Spring Lecture Series in 2010, and an AMS invited address in Syracuse in 2010.
[needs update] In 2010 William P. Minicozzi received the Oswald Veblen Prize in Geometry together with Tobias Colding for their work on minimal surfaces.
[2] In justification of the reward the American Mathematical Society wrote: The 2010 Veblen Prize in Geometry is awarded to Tobias H. Colding and William P. Minicozzi II for their profound work on minimal surfaces.
This contribution led to the resolution of long-standing conjectures of initiated a wave of new results.In 2012 he became a fellow of the American Mathematical Society.