Abstract
We exploit conformal transformations of gluing formulas to realize connections between zeta functions of Laplacians and associated Dirichlet-to-Neumann map zeta functions. Furthermore, the geometric content in gluing formulas is identified and explicit results are given for a three-dimensional manifold.
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Acknowledgements
We thank Peter Gilkey for very helpful discussion surrounding invariance theory. Furthermore, we thank the referees for their remarks, which led to an improvement of the presentation of the results in this article.
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K. Kirsten author was supported by the Baylor University Summer Sabbatical and Research Leave Program. Y. Lee was supported by the National Research Foundation of Korea with the Grant number 2016R1D1A1B01008091.
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Kirsten, K., Lee, Y. The gluing formula, conformal scaling, and geometry. Ann Glob Anal Geom 59, 537–547 (2021). https://doi.org/10.1007/s10455-021-09763-8
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DOI: https://doi.org/10.1007/s10455-021-09763-8
Keywords
- Regularized zeta-determinant
- BFK-gluing formula
- Dirichlet-to-Neumann operator
- Scalar and principal curvatures
- Heat trace asymptotics