The Michigan Mathematical Journal

Asymptotic expansion of the heat kernel for orbifolds

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

Full-text: Open access

Article information

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

First available in Project Euclid: 20 June 2008

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58J50: Spectral problems; spectral geometry; scattering theory [See also 35Pxx] 58J53: Isospectrality


Dryden, Emily B.; Gordon, Carolyn S.; Greenwald, Sarah J.; Webb, David L. Asymptotic expansion of the heat kernel for orbifolds. Michigan Math. J. 56 (2008), no. 1, 205--238. doi:10.1307/mmj/1213972406.

Export citation


  • A. Adem and Y. Ruan, Twisted orbifold K-theory, Comm. Math. Phys. 237 (2003), 533--556.
  • M. Berger, P. Gauduchon, and E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Math., 194, Springer-Verlag, Berlin, 1971.
  • B. C. Berndt and B. P. Yeap, Explicit evaluations and reciprocity theorems for finite trigonometric sums, Adv. in Appl. Math. 29 (2002), 358--385.
  • 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.
  • J. Brüning and M. Lesch, On the spectral geometry of algebraic curves, J. Reine Angew. Math. 474 (1996), 25--66.
  • J. Brüning and R. Seeley, The resolvent expansion for second order regular singular operators, J. Funct. Anal. 73 (1987), 369--429.
  • H.-W. Chen, On some trigonometric power sums, Int. J. Math. Math. Sci. 30 (2002), 185--191.
  • 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.
  • 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.
  • H. Donnelly, Spectrum and the fixed point sets of isometries I, Math. Ann. 224 (1976), 161--170.
  • ------, Asymptotic expansions for the compact quotients of properly discontinuous group actions, Illinois J. Math. 23 (1979), 485--496.
  • P. Doyle and J. P. Rossetti, Isospectral hyperbolic surfaces have matching geodesics, preprint, arXiv:math/0605765v1 [math.DG].
  • 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.
  • C. Farsi, Orbifold spectral theory, Rocky Mountain J. Math. 31 (2001), 215--235.
  • 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.
  • 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.
  • 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.
  • I. Moerdijk and D. Pronk, Orbifolds, sheaves and groupoids, $K$-Theory 12 (1997), 3--21.
  • J. M. Montesinos, Classical tessellations and three-manifolds, Springer-Verlag, Berlin, 1987.
  • E. Park and K. Richardson, The basic Laplacian of a Riemannian foliation, Amer. J. Math. 118 (1996), 1249--1275.
  • L. L. Pennisi, Elements of complex variables, Holt, Rinehart & Winston, New York, 1966.
  • 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.
  • N. Shams, E. A. Stanhope, and D. L. Webb, One cannot hear orbifold isotropy type, Arch. Math. (Basel) 87 (2006), 375--384.
  • E. A. Stanhope, Spectral bounds on orbifold isotropy, Ann. Global Anal. Geom. 27 (2005), 355--375.
  • 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 $$\rangle .$