Intrinsic derivative, curvature estimates and squeezing function
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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 .
KeywordsBergman kernel intrinsic derivative squeezing function
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This work was supported by National Natural Science Foundation of China (Grant Nos. 11371025 and 11671270). The author dedicates the paper for the memory of the late Professor Qikeng Lu, from whom the author has learnt not only mathematics, but also the attitude towards life and truth. The author also thanks the referees’ comments which made the paper more readable.
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