Spinors and mass on weighted manifolds
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220_2022_Article_4420.pdf
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374.75 KB
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Checksum (MD5)
6cc5d183ca8c7a61d9013f4afc036211
Author(s)
Baldauf, Julius
Ozuch, Tristan
Date Issued
July 7, 2022
Publisher
Springer Berlin Heidelberg
Citation
Baldauf, Julius and Ozuch, Tristan. 2022. "Spinors and mass on weighted manifolds."
Version
Final published version
Abstract
Abstract
This paper generalizes classical spin geometry to the setting of weighted manifolds (manifolds with density) and provides applications to the Ricci flow. Spectral properties of the naturally associated weighted Dirac operator, introduced by Perelman, and its relationship with the weighted scalar curvature are investigated. Further, a generalization of the ADM mass for weighted asymptotically Euclidean (AE) manifolds is defined; on manifolds with nonnegative weighted scalar curvature, it satisfies a weighted Witten formula and thereby a positive weighted mass theorem. Finally, on such manifolds, Ricci flow is the gradient flow of said weighted ADM mass, for a natural choice of weight function. This yields a monotonicity formula for the weighted spinorial Dirichlet energy of a weighted Witten spinor along Ricci flow.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00220-022-04420-y
