Intrinsic derivative, curvature estimates and squeezing func

发布时间：2018-02-23 04:28

  本文关键词： Bergman kernel intrinsic derivative squeezing function　出处：《Science China(Mathematics)》2017年06期 　论文类型：期刊论文

【摘要】：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.
[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 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鈥攐ne 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.

【作者单位】： School
【基金】：supported by National Natural Science Foundation of China(Grant Nos.11371025 and 11671270)
【分类号】：O186.1

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