The Atiyah-Patodi-Singer problem for manifolds with general (non-cylindrical) boundary

Gerd Grubb

Journées équations aux dérivées partielles (1991)

  • page 1-11
  • ISSN: 0752-0360

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Grubb, Gerd. "Le problème d'Atiyah-Patodi-Singer pour les variétés à bord générales (non cylindriques)." Journées équations aux dérivées partielles (1991): 1-11. <http://eudml.org/doc/93239>.

@article{Grubb1991,
author = {Grubb, Gerd},
journal = {Journées équations aux dérivées partielles},
keywords = {index of a boundary problem; trace of an operator; Atiyah-Patodi-Singer index},
language = {fre},
pages = {1-11},
publisher = {Ecole polytechnique},
title = {Le problème d'Atiyah-Patodi-Singer pour les variétés à bord générales (non cylindriques)},
url = {http://eudml.org/doc/93239},
year = {1991},
}

TY - JOUR
AU - Grubb, Gerd
TI - Le problème d'Atiyah-Patodi-Singer pour les variétés à bord générales (non cylindriques)
JO - Journées équations aux dérivées partielles
PY - 1991
PB - Ecole polytechnique
SP - 1
EP - 11
LA - fre
KW - index of a boundary problem; trace of an operator; Atiyah-Patodi-Singer index
UR - http://eudml.org/doc/93239
ER -

References

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  1. [ABP]. M. F. Atiyah, R. Bott and V. K. Patodi, On the heat equation and the index theorem, Inventiones Math. 19 (1973), 279-330. Zbl0257.58008MR58 #31287
  2. [APS]. M. F. Atiyah, V. K. Patodi and I. M. Singer, Spectral asymmetry and Riemannian geometry, I, Math. Proc. Camb. Phil. Soc. 77 (1975), 43-69. Zbl0297.58008MR53 #1655a
  3. [BM]. L. Boutet de Monvel, Boundary problems for pseudo-differential operators, Acta Mat. 126 (1971), 11-51. Zbl0206.39401MR53 #11674
  4. [BS]. J. Brüning and R. Seeley, An index theorem for first order regular singular operators, Amer. J. Math. 110 (1988), 659-714. Zbl0664.58035MR89k:58271
  5. [C]. J. Cheeger, Spectral geometry of singular Riemannian spaces, J. Diff. Geom. 18 (1983), 575-657. Zbl0529.58034MR85d:58083
  6. [Ge]. E. Getzler, A short proof of the local Atiyah-Singer index theorem, Topology 25 (1986), 111-117. Zbl0607.58040MR87h:58207
  7. [Gi1]. P. B. Gilkey, The boundary integrand in the formula for the signature and Euler characteristic of a Riemannian manifold with boundary, Adv. in Math. 15 (1975), 334-360. Zbl0306.53042MR51 #4326
  8. [Gi2]. P. B. Gilkey, On the index of geometrical operators for Riemannian manifolds with boundary, (in preparation). Zbl0798.58071
  9. [Gre]. P. Greiner, An asymptotic expansion for the heat equation, Arch. Rat. Mech. Anal. 41 (1971), 163-218. Zbl0238.35038MR48 #9774
  10. [G1]. G. Grubb, «Functional Calculus of Pseudo-Differential Boundary Problems», Progress in Math., Vol. 65, Birkhäuser, Boston, 1986. Zbl0622.35001MR88f:35002
  11. [G2]. G. Grubb, Heat operator trace expansions and index for general Atiyah-Patodi-Singer boundary problems, Copenhagen Univ. Math. Dept. Preprint Series 1991 no. 9. 
  12. [MP]. S. Minakshisundaram and Å. Pleijel, Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds, Canada J. Math. 1 (1949), 242-256. Zbl0041.42701MR11,108b
  13. [R]. J. Roe, «Elliptic Operators, Topology and Asymptotic Methods», Pitman Research Monograph 179, Longman Scientific and Technical, New York, 1988. Zbl0654.58031MR89j:58126
  14. [S1]. R. T. Seeley, Complex powers of an elliptic operator, AMS Proc. Symp. Pure Math. X (1967), 288-307, AMS, Providence R. I. Zbl0159.15504MR38 #6220
  15. [S2]. R. T. Seeley, Analytic extension of the trace associated with elliptic boundary problems, Amer. J. Math. 91 (1969), 963-983. Zbl0191.11901MR42 #877
  16. [S3]. R. T. Seeley, Topics in pseudo-differential operators, «CIME Conference on Pseudo-Differential Operators 1968,» Edizioni Cremonese, Roma, 1969, pp. 169-305. MR41 #3973

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