Le problème d'Atiyah-Patodi-Singer pour les variétés à bord générales (non cylindriques)
Grubb, Gerd
Journées équations aux dérivées partielles, (1991), p. 1-11 / Harvested from Numdam
Publié le : 1991-01-01
@article{JEDP_1991____A8_0,
     author = {Grubb, Gerd},
     title = {Le probl\`eme d'Atiyah-Patodi-Singer pour les vari\'et\'es \`a bord g\'en\'erales (non cylindriques)},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {1991},
     pages = {1-11},
     mrnumber = {93a:58158},
     zbl = {0744.58069},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/JEDP_1991____A8_0}
}
Grubb, Gerd. Le problème d'Atiyah-Patodi-Singer pour les variétés à bord générales (non cylindriques). Journées équations aux dérivées partielles,  (1991), pp. 1-11. http://gdmltest.u-ga.fr/item/JEDP_1991____A8_0/

[ABP]. M. F. Atiyah, R. Bott and V. K. Patodi, On the heat equation and the index theorem, Inventiones Math. 19 (1973), 279-330. | MR 58 #31287 | Zbl 0257.58008

[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. | MR 53 #1655a | Zbl 0314.58016 | Zbl 0297.58008

[BM]. L. Boutet De Monvel, Boundary problems for pseudo-differential operators, Acta Mat. 126 (1971), 11-51. | MR 53 #11674 | Zbl 0206.39401

[BS]. J. Brüning and R. Seeley, An index theorem for first order regular singular operators, Amer. J. Math. 110 (1988), 659-714. | MR 89k:58271 | Zbl 0664.58035

[C]. J. Cheeger, Spectral geometry of singular Riemannian spaces, J. Diff. Geom. 18 (1983), 575-657. | MR 85d:58083 | Zbl 0529.58034

[Ge]. E. Getzler, A short proof of the local Atiyah-Singer index theorem, Topology 25 (1986), 111-117. | MR 87h:58207 | Zbl 0607.58040

[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. | MR 51 #4326 | Zbl 0306.53042

[Gi2]. P. B. Gilkey, On the index of geometrical operators for Riemannian manifolds with boundary, (in preparation). | Zbl 0798.58071

[Gre]. P. Greiner, An asymptotic expansion for the heat equation, Arch. Rat. Mech. Anal. 41 (1971), 163-218. | MR 48 #9774 | Zbl 0238.35038

[G1]. G. Grubb, «Functional Calculus of Pseudo-Differential Boundary Problems», Progress in Math., Vol. 65, Birkhäuser, Boston, 1986. | MR 88f:35002 | Zbl 0622.35001

[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.

[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. | MR 11,108b | Zbl 0041.42701

[R]. J. Roe, «Elliptic Operators, Topology and Asymptotic Methods», Pitman Research Monograph 179, Longman Scientific and Technical, New York, 1988. | MR 89j:58126 | Zbl 0654.58031

[S1]. R. T. Seeley, Complex powers of an elliptic operator, AMS Proc. Symp. Pure Math. X (1967), 288-307, AMS, Providence R. I. | MR 38 #6220 | Zbl 0159.15504

[S2]. R. T. Seeley, Analytic extension of the trace associated with elliptic boundary problems, Amer. J. Math. 91 (1969), 963-983. | MR 42 #877 | Zbl 0191.11901

[S3]. R. T. Seeley, Topics in pseudo-differential operators, «CIME Conference on Pseudo-Differential Operators 1968,» Edizioni Cremonese, Roma, 1969, pp. 169-305. | MR 41 #3973