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arXiv · 2303.01731

The Brylinski beta function of a double layer

Pooja Rani·M. K. Vemuri
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Abstract

An analogue of Brylinski's knot beta function is defined for a compactly supported (Schwartz) distribution $T$ on $d$-dimensional Euclidean space. This is a holomorphic function on a right half-plane. If $T$ is a (uniform) double-layer on a compact smooth hypersurface, then the beta function has an analytic continuation to the complex plane as a meromorphic function, and the residues are integrals of invariants of the second fundamental form. The first few residues are computed when $d=2$ and $d=3$.

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Pooja Rani, M. K. Vemuri. 2023-03-03. The Brylinski beta function of a double layer. https://arxiv.org/abs/2303.01731

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