He has been the recipient of a
Guggenheim Fellowship in 1989 and a
Sloan Research Fellowship. In 2002, he was an invited speaker in the Differential Geometry section of the
International Congress of Mathematicians in Beijing, where he spoke on the subject of harmonic functions on Riemannian manifolds. In 2007, he was elected a member of the
American Academy of Arts and Sciences, which cited his "pioneering" achievements in geometric analysis, and in particular his paper with Yau on the differential Harnack inequalities, and its application by
Richard S. Hamilton and
Grigori Perelman in the proof of the
Poincaré conjecture and
geometrization conjecture. ==Notable publications==