Intrinsic derivative, curvature estimates and squeezing function

Abstract

This survey paper consists of two folds. First of all, we recall the concept of intrinsic derivative which was introduced by Lu (1979) and the related works due to Lu in his last ten years, including the holomorphically isometric embedding into the infinite dimensional Grassmann manifold and the Bergman curvature estimates for bounded domains in ℂn. Inspired by Lu’s idea, we give the lower and upper bounds estimates for the Bergman curvatures in terms of the squeezing function—one concept originally introduced by Deng et al. (2012). Finally, we survey some recent progress on the asymptotic behaviors for Bergman curvatures near the strictly pseudoconvex boundary points and present some open problems on the squeezing functions of bounded domains in ℂn.