Communications in Analysis and Geometry

Volume 11 (2003)

Number 3

Stability, Energy Functionals, and Kähler-Einstein Metrics

Pages: 565 – 597



D. H. Phong

Jacob Sturm


In this paper, building on the earlier work of Yau [Y3, Y4], Tian [T1,T2] and Zhang [Z], we construct a semi-norm ∥∙ ∥# which is defined on the full space H0(Gr,O(d)) of polynomials of degree d on the Grassmann variety Gr, and which gives exactly the Mabuchi functional when restricted to the space of Chow vectors, up to a specific current supported on the singular locus of the Chow variety.

Full Text (PDF format)