On the Laplace–Beltrami operator on compact complex spaces
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Abstract:
Let $(X,h)$ be a compact and irreducible Hermitian complex space of complex dimension $v>1$. In this paper we show that the Friedrichs extension of both the Laplace–Beltrami operator and the Hodge–Kodaira Laplacian acting on functions has discrete spectrum. Moreover, we provide some estimates for the growth of the corresponding eigenvalues, and we use these estimates to deduce that the associated heat operators are trace class. Finally we give various applications to the Hodge–Dolbeault operator and to the Hodge–Kodaira Laplacian in the setting of Hermitian complex spaces of complex dimension $2$.References
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Additional Information
- Francesco Bei
- Affiliation: Dipartimento di Matematica, Università degli Studi di Padova, Padova, Italy
- MR Author ID: 1044337
- Email: bei@math.unipd.it; francescobei27@gmail.com
- Received by editor(s): April 22, 2018
- Received by editor(s) in revised form: March 13, 2019
- Published electronically: May 30, 2019
- Additional Notes: This work was performed within the framework of the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program “Investissements d’Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR)
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 8477-8505
- MSC (2010): Primary 32W05, 32W50, 35P15; Secondary 58J35
- DOI: https://doi.org/10.1090/tran/7848
- MathSciNet review: 4029702