Asymptotic expansion of the heat kernel for orbifolds
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Asymptotic expansion of the heat kernel for orbifolds

Emily B. Dryden, Carolyn S. Gordon, Sarah J. Greenwald, and David L. Webb

Source: Michigan Math. J. Volume 56, Issue 1 (2008), 205-238.

Primary Subjects: 58J50, 58J53

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Permanent link to this document: http://projecteuclid.org/euclid.mmj/1213972406
Digital Object Identifier: doi:10.1307/mmj/1213972406

References

A. Adem and Y. Ruan, Twisted orbifold K-theory, Comm. Math. Phys. 237 (2003), 533--556.
Mathematical Reviews (MathSciNet): MR1993337
M. Berger, P. Gauduchon, and E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Math., 194, Springer-Verlag, Berlin, 1971.
Mathematical Reviews (MathSciNet): MR282313
B. C. Berndt and B. P. Yeap, Explicit evaluations and reciprocity theorems for finite trigonometric sums, Adv. in Appl. Math. 29 (2002), 358--385.
Mathematical Reviews (MathSciNet): MR1942629
Digital Object Identifier: doi:10.1016/S0196-8858(02)00020-9
T. P. Branson and P. B. Gilkey, The asymptotics of the Laplacian on a manifold with boundary, Comm. Partial Differential Equations 15 (1990), 245--272.
Mathematical Reviews (MathSciNet): MR1032631
Digital Object Identifier: doi:10.1080/03605309908820686
J. Brüning and M. Lesch, On the spectral geometry of algebraic curves, J. Reine Angew. Math. 474 (1996), 25--66.
Mathematical Reviews (MathSciNet): MR1390691
J. Brüning and R. Seeley, The resolvent expansion for second order regular singular operators, J. Funct. Anal. 73 (1987), 369--429.
Mathematical Reviews (MathSciNet): MR899656
Digital Object Identifier: doi:10.1016/0022-1236(87)90073-5
H.-W. Chen, On some trigonometric power sums, Int. J. Math. Math. Sci. 30 (2002), 185--191.
Mathematical Reviews (MathSciNet): MR1905420
Digital Object Identifier: doi:10.1155/S0161171202007731
Y.-J. Chiang, Spectral geometry of $ V$-manifolds and its application to harmonic maps, Differential geometry: Partial differential equations on manifolds (Los Angeles, 1990), Proc. Sympos. Pure Math., 54, pp. 93--99, Amer. Math. Soc., Providence, RI, 1993.
Mathematical Reviews (MathSciNet): MR1216577
Zentralblatt MATH: 0806.58005
J. H. Conway, The orbifold notation for surface groups, Groups, combinatorics and geometry (Durham, 1990), London Math. Soc. Lecture Note Ser., 165, pp. 438--447, Cambridge Univ. Press, Cambridge, 1992.
Mathematical Reviews (MathSciNet): MR1200280
Zentralblatt MATH: 0835.20048
H. Donnelly, Spectrum and the fixed point sets of isometries I, Math. Ann. 224 (1976), 161--170.
Mathematical Reviews (MathSciNet): MR420743
Digital Object Identifier: doi:10.1007/BF01436198
------, Asymptotic expansions for the compact quotients of properly discontinuous group actions, Illinois J. Math. 23 (1979), 485--496.
Mathematical Reviews (MathSciNet): MR537804
P. Doyle and J. P. Rossetti, Isospectral hyperbolic surfaces have matching geodesics, preprint, arXiv:math/0605765v1 [math.DG].
Mathematical Reviews (MathSciNet): MR2413218
E. B. Dryden and A. Strohmaier, Huber's theorem for hyperbolic orbisurfaces, Canad. Math. Bull. (to appear).
J. J. Duistermaat and J. A. C. Kolk, Lie groups, Springer-Verlag, Berlin, 2000.
Mathematical Reviews (MathSciNet): MR1738431
Zentralblatt MATH: 0955.22001
C. Farsi, Orbifold spectral theory, Rocky Mountain J. Math. 31 (2001), 215--235.
Mathematical Reviews (MathSciNet): MR1821378
Digital Object Identifier: doi:10.1216/rmjm/1008959678
Project Euclid: euclid.rmjm/1181070249
M. E. Fisher, Problem 69-14, SIAM Rev. 13 (1971), 116--119.
J. B. Gil, Full asymptotic expansion of the heat trace for non-self-adjoint elliptic cone operators, Math. Nachr. 250 (2003), 25--57.
Mathematical Reviews (MathSciNet): MR1956600
Digital Object Identifier: doi:10.1002/mana.200310020
C. S. Gordon and J. P. Rossetti, Boundary volume and length spectra of Riemannian manifolds: What the middle degree Hodge spectrum doesn't reveal, Ann. Inst. Fourier (Grenoble) 53 (2003), 2297--2314.
Mathematical Reviews (MathSciNet): MR2044174
I. Moerdijk, Orbifolds as groupoids, an introduction, Orbifolds in mathematics and physics (Madison, 2001), Contemp. Math., 310, pp. 205--222, Amer. Math. Soc., Providence, RI, 2002.
Mathematical Reviews (MathSciNet): MR1950948
Zentralblatt MATH: 1041.58009
I. Moerdijk and D. Pronk, Orbifolds, sheaves and groupoids, $K$-Theory 12 (1997), 3--21.
Mathematical Reviews (MathSciNet): MR1466622
Digital Object Identifier: doi:10.1023/A:1007767628271
J. M. Montesinos, Classical tessellations and three-manifolds, Springer-Verlag, Berlin, 1987.
Mathematical Reviews (MathSciNet): MR915761
Zentralblatt MATH: 0626.57002
E. Park and K. Richardson, The basic Laplacian of a Riemannian foliation, Amer. J. Math. 118 (1996), 1249--1275.
Mathematical Reviews (MathSciNet): MR1420923
Zentralblatt MATH: 0865.58047
Digital Object Identifier: doi:10.1353/ajm.1996.0053
L. L. Pennisi, Elements of complex variables, Holt, Rinehart & Winston, New York, 1966.
Mathematical Reviews (MathSciNet): MR206213
K. Richardson, Traces of heat operators on Riemannian foliations, preprint.
J. P. Rossetti, D. Schueth, and M. Weilandt, Isospectral orbifolds with different maximal isotropy orders, Ann. Global Anal. Geom. (to appear).
I. Satake, The Gauss--Bonnet theorem for $V$-manifolds, J. Math. Soc. Japan 9 (1957), 464--492.
Mathematical Reviews (MathSciNet): MR95520
Zentralblatt MATH: 0080.37403
N. Shams, E. A. Stanhope, and D. L. Webb, One cannot hear orbifold isotropy type, Arch. Math. (Basel) 87 (2006), 375--384.
Mathematical Reviews (MathSciNet): MR2263484
Digital Object Identifier: doi:10.1007/s00013-006-1748-0
E. A. Stanhope, Spectral bounds on orbifold isotropy, Ann. Global Anal. Geom. 27 (2005), 355--375.
Mathematical Reviews (MathSciNet): MR2155380
Digital Object Identifier: doi:10.1007/s10455-005-1584-7
E. A. Stanhope and A. Uribe, The trace formula for orbifolds, preprint.
W. P. Thurston, Geometry and topology of $3$-manifolds, Lecture notes, 1980, $\langle $http://www.msri.org/publications/books/gt3m/$\rangle .$
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