The aim of this article is to extend a theorem by Cheeger and Müller to spaces with isolated conical singularities by generalizing the proof of Bismut and Zhang to the singular setting. The main tools in this approach are the Witten deformation and local index techniques.
"An extension of a theorem by Cheeger and Müller to spaces with isolated conical singularities." Duke Math. J. 169 (13) 2501 - 2570, 15 September 2020. https://doi.org/10.1215/00127094-2020-0008