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- W2949948867 abstract "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 $Delta$ 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 $pi$ 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 $$ Tr cos t sqrtDelta in C^{-n-0}(RR) cap C^{-1-0}(RRbackslash GEOM) cap C^infty(RRbackslash DIFF).$$ This generalizes a classical result of Chazarain and Duistermaat-Guillemin on boundaryless manifolds, which in turn follows from Poisson summation in the case $X=S^1.$" @default.
- W2949948867 created "2019-06-27" @default.
- W2949948867 creator A5085412939 @default.
- W2949948867 date "2002-02-25" @default.
- W2949948867 modified "2023-09-27" @default.
- W2949948867 title "A Poisson relation for conic manifolds" @default.
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