Bulletin of the
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ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2023; 60(6): 1539-1553

Online first article September 18, 2023      Printed November 30, 2023

https://doi.org/10.4134/BKMS.b220735

Copyright © The Korean Mathematical Society.

Volume density asymptotics of central harmonic spaces

Peter Gilkey, JeongHyeong Park

University of Oregon; Sungkyunkwan University

Abstract

We show the asymptotics of the volume density function in the class of central harmonic manifolds can be specified arbitrarily and do not determine the geometry.

Keywords: Harmonic spaces, density function, radial harmonic function, rank 1 symmetric spaces, Damek--Ricci spaces, conformal invariants, Weyl conformal tensor

MSC numbers: 53C21

Supported by: The research of P. Gilkey was partially supported by grant PID2020-114474GB-I0 (Spain). The research of J. H. Park was partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2019R1A2C1083957).

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