| 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 Words:
Laplace-Beltrami operator classical bounded symmetric domains K\"{a}hler metric
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| Fund Project: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). |
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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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