Infimum of the Spectrum of Laplace-Beltrami Operator on Classical Bounded Symmetric Domains with Bergman Metric
Received:July 19, 2017  Revised:September 10, 2018
Key Word: Laplace-Beltrami operator   classical bounded symmetric domains   K\"{a}hler metric  
Fund ProjectL:Supported by the Natural Science Foundation of Guangxi Province (Grant Nos.2015GXNSFBA139019; 2016GXNSFDA380031), Guangxi Key Laboratory of Cryptography and Information Security (Grant No.GCIS201612), National Natural Science Foundation of China (Grant No.11662001), Research Foundation of Fujian Province for Young and Middle-aged Teachers (Grant No.JAT170467) and the Research Foundation of Minjiang University for the Introduction of Talents (Grant No.MJY1706).
Author NameAffiliation
Sujuan LONG School of Mathematics and Data Science, Minjiang University, Fujian 350108, P. R. China
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guangxi 541004, P. R. China 
Kezan LI School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guangxi 541004, P. R. China 
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Abstract:
      In this paper, we estimate the infimum of the spectrum of the Laplace-Beltrami operator with K\"ahler metric on the classical bounded symmetric domains. We will give an explicit range for the infimum of the spectrum of the Laplace-Beltrami operator on the second type classical bounded symmetric domains. In particular, for those domains with rank $1$, we obtain an explicit formula, which agrees with a previously known result.
Citation:
DOI:10.3770/j.issn:2095-2651.2019.01.005
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