Analytic Torsion on Manifolds with Edges
By Rafe Mazzeo, Boris Vertman. 2011
66 citations recorded by the source corpus.
Let (M,g) be an odd-dimensional incomplete compact Riemannian singular space with a simple edge singularity. We study the analytic torsion on M, and in particular consider how it depends on the metric g. If g is an admissible edge metric, we prove that the torsion zeta function is holomorphic near s = 0, hence the torsion is well-defined, but possibly depends on g. In general dimensions, we prove that the analytic torsion depends only on the asymptotic structure of g near the singular stratum of M; when the dimension of the edge is odd, we prove that the analytic torsion is independent of the choice of admissible edge metric. The main tool is the construction, via the methodology of geometric microlocal analysis, of the heat kernel for the Friedrichs extension of the Hodge Laplacian in all degrees. In this way we obtain detailed asymptotics of this heat kernel and its trace.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ff079f4bbfe59a714d8ee792d7fd9261dcb8ad37
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Rafe Mazzeo
- Yanir A. Rubinstein
- Thalia D. Jeffres
- Robert J. Berman
- Chi Li
- G. Tian
- Tam'as Darvas
- Y. Odaka
In Mathematical Physics
Citations in the corpus
- Kahler-Einstein metrics with edge singularities (2011, background): “ing a standard approximation argument with a cut-off function vanishing in a neighborhood of D. We also give a more conceptual proof. The heat kernel etL for the Friedrichs extension is constructed in [47], and it is proved there that etLf∈ A0 phg for any f∈ L2, and of course lies in DFr(L), for all ”