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Semicontinuity Theorems for Holomorphic and CR Automorphism Groups

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Geometric Complex Analysis

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 246))

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Abstract

We review the semicontinuity property for automorphism groups of CR manifolds proved in Joo (Pac J Math 285:225–241, 2016 [19]) which belongs to the line of research on the semicontinuity for Riemmanian isometry groups and holomorphic automorphism groups of domains Ebin (Proceedings of symposia in pure mathematics, pp 11–40, 1968 [6]), Greene and Kim (Math Z 277:909–916, 2014 [10]), Greene et al. (Pac J Math 262:365–395, 2013 [12]), Greene and Krantz (Math Ann 261:425–446, 1982 [13]), Kim (Arch Math (Basel) 49:450–455, 1987 [21]), Krantz (Real Anal Exch 36, 421–433, 2010/11 [22]). A brief explanation of the proof and some related open problems as well as the motivation of the study are provided.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Kingdom of Saudi Arabia

    Jae-Cheon Joo

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  1. Jae-Cheon Joo
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Correspondence to Jae-Cheon Joo .

Editor information

Editors and Affiliations

  1. Department of Mathematics Education, Kyungnam University, Changwon, Korea (Republic of)

    Jisoo Byun

  2. Department of Mathematics, Pusan National University, Busan, Korea (Republic of)

    Hong Rae Cho

  3. Center for Mathematical Challenges, Korea Institute for Advanced Study, Seoul, Korea (Republic of)

    Sung Yeon Kim

  4. Department of Mathematics, Gyeongsang National University, Jinju, Korea (Republic of)

    Kang-Hyurk Lee

  5. Department of Mathematics, Kyung Hee University, Seoul, Korea (Republic of)

    Jong-Do Park

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Joo, JC. (2018). Semicontinuity Theorems for Holomorphic and CR Automorphism Groups. In: Byun, J., Cho, H., Kim, S., Lee, KH., Park, JD. (eds) Geometric Complex Analysis. Springer Proceedings in Mathematics & Statistics, vol 246. Springer, Singapore. https://doi.org/10.1007/978-981-13-1672-2_16

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