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Harmonic Spaces and Density Functions

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Abstract

We use the density function of a harmonic space to obtain estimates for the eigenvalues of the Jacobi operator; when these estimates are sharp, then the harmonic space is a symmetric Osserman space.

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Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MSIT) (NRF-2019R1A2C1083957) and by Project MTM2016-75897-P (AEI/FEDER, UE). The authors acknowledge with gratitude useful conversations with Professors Eduardo García-Río and Mitsuhiro Itoh concerning the paper. The second author thanks the Department of Mathematics, UC Berkeley, for the hospitality provided during the visit when this work was carried out.

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Authors and Affiliations

  1. Mathematics Department, University of Oregon, Eugene, OR, 97403-1222, USA

    P. B. Gilkey

  2. Department of Mathematics, Sungkyunkwan University, Suwon, 16419, Korea

    J. H. Park

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  1. P. B. Gilkey
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  2. J. H. Park
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Correspondence to J. H. Park.

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Gilkey, P.B., Park, J.H. Harmonic Spaces and Density Functions. Results Math 75, 121 (2020). https://doi.org/10.1007/s00025-020-01248-7

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