대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제57권5호
  • /
  • Pages.1241-1249
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  • 2020
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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A NOTE ON THE BOUNDARY BEHAVIOUR OF THE SQUEEZING FUNCTION AND FRIDMAN INVARIANT

  • Kim, Hyeseon (Research Institute of Mathematics Seoul National University) ;
  • Mai, Anh Duc (Faculty of Mathematics Physics and Informatics Tay Bac University) ;
  • Nguyen, Thi Lan Huong (Department of Mathematics Hanoi University of Mining and Geology) ;
  • Ninh, Van Thu (Department of Mathematics Vietnam National University at Hanoi)
  • 투고 : 2019.10.14
  • 심사 : 2020.05.14
  • 발행 : 2020.09.30
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초록

Let Ω be a domain in ℂn. Suppose that ∂Ω is smooth pseudoconvex of D'Angelo finite type near a boundary point ξ0 ∈ ∂Ω and the Levi form has corank at most 1 at ξ0. Our goal is to show that if the squeezing function sΩ(𝜂j) tends to 1 or the Fridman invariant hΩ(𝜂j) tends to 0 for some sequence {𝜂j} ⊂ Ω converging to ξ0, then this point must be strongly pseudoconvex.

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참고문헌

  1. F. Berteloot, Characterization of models in $C^2$ by their automorphism groups, Internat. J. Math. 5 (1994), no. 5, 619-634. https://doi.org/10.1142/S0129167X94000322
  2. D. Borah and D. Kar, Boundary behavior of the Caratheodory and Kobayashi-Eisenman volume elements, Illinois J. Math. 64 (2020), no. 2, 151-168. https://doi.org/10.1215/00192082-8303461
  3. S. Cho, Boundary behavior of the Bergman kernel function on some pseudoconvex domains in $C^n$, Trans. Amer. Math. Soc. 345 (1994), no. 2, 803-817. https://doi.org/10.2307/2154999
  4. F. Deng, Q. Guan, and L. Zhang, Some properties of squeezing functions on bounded domains, Pacific J. Math. 257 (2012), no. 2, 319-341. https://doi.org/10.2140/pjm.2012.257.319
  5. F. Deng, Q. Guan, and L. Zhang, Properties of squeezing functions and global transformations of bounded domains, Trans. Amer. Math. Soc. 368 (2016), no. 4, 2679-2696. https://doi.org/10.1090/tran/6403
  6. K. Diederich, J. E. Fornss, and E. F. Wold, Exposing points on the boundary of a strictly pseudoconvex or a locally convexifiable domain of finite 1-type, J. Geom. Anal. 24 (2014), no. 4, 2124-2134. https://doi.org/10.1007/s12220-013-9410-0
  7. D. T. Do and V. T. Ninh, Characterization of domains in $C^n$ by their noncompact automorphism groups, Nagoya Math. J. 196 (2009), 135-160. https://doi.org/10.1017/S002776300000982X
  8. R. E. Greene and S. G. Krantz, Biholomorphic self-maps of domains, in Complex analysis, II (College Park, Md., 1985-86), 136-207, Lecture Notes in Math., 1276, Springer, Berlin, 1987. https://doi.org/10.1007/BFb0078959
  9. S. Joo and K.-T. Kim, On boundary points at which the squeezing function tends to one, J. Geom. Anal. 28 (2018), no. 3, 2456-2465. https://doi.org/10.1007/s12220-017-9910-4
  10. K.-T. Kim and L. Zhang, On the uniform squeezing property of bounded convex domains in $C^n$, Pacific J. Math. 282 (2016), no. 2, 341-358. https://doi.org/10.2140/pjm.2016.282.341
  11. P. Mahajan and K. Verma, Some aspects of the Kobayashi and Caratheodory metrics on pseudoconvex domains, J. Geom. Anal. 22 (2012), no. 2, 491-560. https://doi.org/10.1007/s12220-010-9206-4
  12. P. Mahajan and K. Verma, A comparison of two biholomorphic invariants, Internat. J. Math. 30 (2019), no. 1, 1950012, 16 pp. https://doi.org/10.1142/S0129167X19500125
  13. N. Nikolov, Behavior of the squeezing function near h-extendible boundary points, Proc. Amer. Math. Soc. 146 (2018), no. 8, 3455-3457. https://doi.org/10.1090/proc/14049
  14. N. Nikolov and K. Verma, On the Squeezing Function and Fridman Invariants, J. Geom. Anal. 30 (2020), no. 2, 1218-1225. https://doi.org/10.1007/s12220-019-00237-9
  15. V. T. Ninh and Q. D. Nguyen, Some properties of h-extendible domains in $C^{n+1}$, J. Math. Anal. Appl. 485 (2020), no. 2, 123810. https://doi.org/10.1016/j.jmaa.2019.123810
  16. J. Y. Yu, Peak functions on weakly pseudoconvex domains, Indiana Univ. Math. J. 43 (1994), no. 4, 1271-1295. https://doi.org/10.1512/iumj.1994.43.43055