Mayer-Vietoris Formula for Determinants of Elliptic Operators of Laplace-Beltrami Type (after Burghelea, Friedlander and Kappeler)
Yoonweon Lee (Ohio State University)
TL;DR
This paper presents a simplified approach to the Mayer-Vietoris formula for regularized determinants of Laplace-Beltrami elliptic operators, aiding applications in geometric torsion calculations.
Contribution
It offers a concise derivation of the Mayer-Vietoris formula for elliptic operators, enhancing computational efficiency in geometric analysis.
Findings
Simplified proof of the Mayer-Vietoris formula
Application to torsion-related problems
Clarification of determinant regularization techniques
Abstract
The purpose of this note is to provide a short cut presentation of a Mayer-Vietoris formula due to Burghelea-Friedlander-Kappeler for the regularized determinant in the case of elliptic operators of Laplace Beltrami type in the form typically needed in applications to torsion.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNumerical methods in inverse problems · Algebraic and Geometric Analysis · Matrix Theory and Algorithms