Selected Expository Works of Shing-tung Yau With Commentary

Comprising volumes 28 and 29 of the ALM series, this outstanding collection presents all the survey papers of Shing-Tung Yau published to date (through 2013), each with Yau’s own commentary. Among these are several papers not otherwise easily accessible. Also presented are several commentaries on Yau’s work written by outstanding scholars from around the world especially for publication here.

Shing-Tung Yau’s work is mainly in differential geometry, and he is one of the originators of the broad subject of geometric analysis - in which he remains one of the most active participants. His contributions have had an influence on both physics and mathematics, and he has long been active at the interface between geometry and theoretical physics. His proof of the positive energy theorem in general relativity demonstrated - sixty years after its discovery - that Einstein’s theory is consistent and stable. His proof of the Calabi conjecture allowed physicists - using Calabi-Yau compactification - to show that string theory is a viable candidate for a unified theory of nature. Calabi-Yau manifolds are part of the standard toolkit of string theorists today. He was awarded the Fields Medal in 1982 and the Wolf Prize in 2010, and has received many other honors.

The Selected Expository Works of Shing-Tung Yau with Commentary provides the reader with systematic commentary on all aspects of mathematics by a contemporary master. The reader can thereby see the world of mathematics through his particular perspective, and gain understanding of the motivation and evolution of mathematical ideas.