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 holomorphicall...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 C^n. 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 C^n.展开更多
In this paper,the authors introduce the notion of generalized squeezing function and study the basic properties of generalized squeezing functions and Fridman invariants.They also study the comparison of these two inv...In this paper,the authors introduce the notion of generalized squeezing function and study the basic properties of generalized squeezing functions and Fridman invariants.They also study the comparison of these two invariants,in terms of the so-called quotient invariant.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11371025 and 11671270)
文摘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 C^n. 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 C^n.
基金supported by the National Natural Science Foundation of China(No.11871333)
文摘In this paper,the authors introduce the notion of generalized squeezing function and study the basic properties of generalized squeezing functions and Fridman invariants.They also study the comparison of these two invariants,in terms of the so-called quotient invariant.
