Volume density asymptotics of central harmonic spaces
Peter B. Gilkey, JeongHyeong Park
TL;DR
This paper demonstrates that the volume density function's asymptotic behavior in central harmonic manifolds can be arbitrarily specified and does not uniquely determine the manifold's geometry.
Contribution
It reveals that volume density asymptotics are not sufficient to characterize the geometry of central harmonic spaces.
Findings
Volume density asymptotics can be arbitrarily prescribed.
Asymptotics do not uniquely determine the manifold's geometry.
Central harmonic spaces exhibit flexible volume density behaviors.
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.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Stochastic processes and statistical mechanics