Room 202, Astronomy-Mathematics Building, NTU

(台灣大學天文數學館 202室)

Construction of Global CR Invariants via Cheng-Yau Metric

Taiji Marugame (University of Tokyo)

Abstract

Strictly pseudoconvex domains in a Stein manifold admit a complete Kahler-Einstein metric called the Cheng-Yau metric. In this talk, I present two methods of constructing global CR invariants of the boundary using this metric. The first is the renormalized Chern-Gauss-Bonnet formula, which gives a higher dimensional generalization of the Burns-Epstein invariant. The second is the renormalized volume, which is shown to agree with the integral of the CR Q-prime curvature of the boundary. The second construction is joint work with K. Hirachi and Y. Matsumoto.