Selected expository works of Shing-Tung Yau with commentary. Volume II
For the first part of this review see Volume I [Zbl 1401.01045].NEWLINENEWLINEIn \textbf{Volume II}, 11 papers of Yau are presented, each article having an introductory commentary (including also some history) by S.-T. Yau. The expository papers of Yau are arranged according to the years of publication. The following topics studied by Yau and his co-workers are pointed-out:NEWLINENEWLINE\smallskipNEWLINENEWLINE- Perspectives on geometric analysis;NEWLINENEWLINE\smallskipNEWLINENEWLINE- A survey on Calaby-Yau manifolds;NEWLINENEWLINE\smallskipNEWLINENEWLINE- Linear waves in the Kerr geometry: a mathematical voyage to black hole physics;NEWLINENEWLINE\smallskipNEWLINENEWLINE- Recent development on the geometry of Teichmüller and moduli spaces of Riemannian surfaces;NEWLINENEWLINE\smallskipNEWLINENEWLINE- Deformation of Kähler-Einstein metric;NEWLINENEWLINE\smallskipNEWLINENEWLINE- String theory and the geometry of the universe's hidden dimensions;NEWLINENEWLINE\smallskipNEWLINENEWLINE- Shiing-Shen Chern (1911--2004);NEWLINENEWLINE\smallskipNEWLINENEWLINE- A survey on recent development in computational quasi-conformal geometry;NEWLINENEWLINE\smallskipNEWLINENEWLINE- Recent development of computational conformal geometry;NEWLINENEWLINE\smallskipNEWLINENEWLINE- Mirror symmetry and localizations;NEWLINENEWLINE\smallskipNEWLINENEWLINE- Non-Kähler Calabi-Yau manifolds.NEWLINENEWLINEThis volume continues with commentaries of other authors on the work of Yau and ends with a list of publication of Yau and a list of his Ph.D. and postdoctoral students.NEWLINENEWLINEThe two volumes represent indeed excellent material in the wonderful field of mathematics. Yau's dedication to mathematics enriches many subjects, as differential geometry, differential equations, topology, algebraic geometry and mathematical physics.NEWLINENEWLINEFrom the publisher's description: ``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.''
scientific article; zbMATH DE number 6359381