By S.T. Yau

The Surveys in Differential Geometry are vitamins to the magazine of Differential Geometry, that are released by way of foreign Press. They contain major invited papers combining unique examine and overviews of the most up-tp-date study in particular components of curiosity to the becoming magazine of Differential Geometry group. The survey volumes function carrying on with references, inspirations for brand spanking new examine, and introductions to the diversity of themes of curiosity to differential geometers. those vitamins are released every year on the grounds that 1999. This quantity arises out of the convention subsidized via the magazine of Differential Geometry and held at Harvard college to honor the 4 mathematicians who based Index thought. loads of geometers collected for this old get together which integrated a variety of tributes and recollections so as to be released in a separate quantity. The 4 founders of the Index concept - Michael Atiyah, Raoul Bott, Frederich Hirzebruch, and Isadore Singer - are resources of notion, mentors and academics for the opposite audio system and contributors on the convention. The larger-than-usual measurement of this quantity derives without delay from the super admire and admiration for the honorees. desk of Contents: 1. Projective planes, Severi types and spheres - M. Atiyah and J. Berndt 2. Degeneration of Einstein metrics and metrics with specific holonomy - J. Cheeger three. The min-max building of minimum surfaces - T. H. Colding and C. De Lellis four. common quantity bounds in Riemannian manifolds - C. B. Croke and M. Katz five. A Kawamata-Viehweg vanishing theorem on compact Kahler manifolds - J.-P. Demailly and T. Peternell 6. second maps in differential geometry - S. ok. Donaldson 7. neighborhood pressure for cocycles - D. Fisher and G. A. Margulis eight. Einstein metrics, four-manifolds, and differential topology - C. LeBrun nine. Topological quantum box concept for Calabi-Yau threefolds and $G_2$-manifold - N. C. Leung 10. Geometric leads to classical minimum floor conception - W. H. Meeks III eleven. On international lifestyles of wave maps with severe regularity - A. Nahmod 12. Discreteness of minimum versions of Kodaira size 0 and subvarieties of moduli stacks - E. Viehweg and ok. Zuo thirteen. Geometry of the Weil-Petersson final touch of Teichm??ller area - S. A. Wolpert