A Poisson relation for conic manifolds
| dc.creator | Wunsch, Jared | |
| dc.date | 2002-02-25 | |
| dc.date | 2002-09-24 | |
| dc.date.accessioned | 2026-07-07T04:46:41Z | |
| dc.date.available | 2026-07-07T04:46:41Z | |
| dc.description | Let $X$ be a compact Riemannian manifold with conic singularities, i.e. a Riemannian manifold whose metric has a conic degeneracy at the boundary. Let $Δ$ be the Friedrichs extension of the Laplace-Beltrami operator on $X.$ There are two natural ways to define geodesics passing through the boundary: as ``diffractive'' geodesics which may emanate from $\partial X$ in any direction, or as ``geometric'' geodesics which must enter and leave $\partial X$ at points which are connected by a geodesic of length $π$ in $\partial X.$ Let $\DIFF=\{0\} \cup \{\pm lengths of closed diffractive geodesics\}$ and $\GEOM=\{0\} \cup \{\pm lengths of closed geometric geodesics\}.$ We show that $$ \Tr \cos t \sqrtΔ\in C^{-n-0}(\RR) \cap C^{-1-0}(\RR\backslash \GEOM) \cap C^\infty(\RR\backslash \DIFF).$$ This generalizes a classical result of Chazarain and Duistermaat-Guillemin on boundaryless manifolds, which in turn follows from Poisson summation in the case $X=S^1.$ | |
| dc.description | Exposition substantially improved. 1 figure added. Title changed | |
| dc.identifier | https://arxiv.org/abs/math/0202264 | |
| dc.identifier | http://arxiv.org/abs/math/0202264 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63430 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Spectral Theory | |
| dc.subject | 58J47, 58J50, 35L05 | |
| dc.title | A Poisson relation for conic manifolds | |
| dc.type | text |