Communications in Analysis and Geometry

Volume 20 (2012)

Number 5

Geometry of singular space

Pages: 1097 – 1134

DOI: http://dx.doi.org/10.4310/CAG.2012.v20.n5.a7

Author

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Mass., U.S.A.)

Abstract

This paper grew out of my talk for the inauguration of the Riemann Center in Hanover, Germany. In an attempt to understand what Riemann said in his famous paper in 1854 on the foundation of geometry, I propose a theory of geometry that hopefully can be used to understand singular space that may still satisfy the Einstein equation in a generalized sense. Some calculations are made in the appendix that allow us to perform Hodge theory, to calculate the heat kernel within our abstract framework.

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