The Brylinski beta function of a coaxial layer
Differential Geometry
2024-10-02 v1
Abstract
In [Pooja Rani and M. K. Vemuri, The Brylinski beta function of a double layer, Differential Geom. Appl. \textbf{92}(2024)], an analogue of Brylinski's knot beta function was defined for a compactly supported (Schwartz) distribution on Euclidean space. Here we consider the Brylinski beta function of the distribution defined by a coaxial layer on a submanifold of Euclidean space. We prove that it has an analytic continuation to the whole complex plane as a meromorphic function with only simple poles, and in the case of a coaxial layer on a space curves, we compute some of the residues in terms of the curvature and torsion.
Keywords
Cite
@article{arxiv.2410.00555,
title = {The Brylinski beta function of a coaxial layer},
author = {Pooja Rani and M. K. Vemuri},
journal= {arXiv preprint arXiv:2410.00555},
year = {2024}
}