@article{SIGMA_2007_3_a103,
author = {William J. Ugalde},
title = {Some {Conformal} {Invariants} from the {Noncommutative} {Residue} for {Manifolds} with {Boundary}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2007},
volume = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a103/}
}
TY - JOUR AU - William J. Ugalde TI - Some Conformal Invariants from the Noncommutative Residue for Manifolds with Boundary JO - Symmetry, integrability and geometry: methods and applications PY - 2007 VL - 3 UR - http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a103/ LA - en ID - SIGMA_2007_3_a103 ER -
William J. Ugalde. Some Conformal Invariants from the Noncommutative Residue for Manifolds with Boundary. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a103/
[1] Adler M., “On a trace functional for formal pseudodifferential operators and the symplectic structure of the Korteweg–de Vries type equations”, Invent. Math., 50 (1979), 219–248 | DOI | MR | Zbl
[2] Bär C., “Conformal structures in noncommutative geometry”, J. Noncommut. Geom., 1 (2007), 385–395 ; arXiv:0704.2119 | DOI | MR | Zbl
[3] Boutet de Monvel L., “Boundary problems for pseudo-differential operators”, Acta Math., 126 (1971), 11–51 | DOI | MR | Zbl
[4] Connes A., “The action functional in noncommutative-geometry”, Comm. Math. Phys., 117 (1988), 673–683 | DOI | MR | Zbl
[5] Connes A., “Quantized calculus and applications”, Proceedings of the XIth International Congress of Mathematical Physics, International Press, Cambridge, MA, 1995, 15–36 | MR | Zbl
[6] Connes A., Noncommutative geometry, Academic Press, London and San Diego, 1994 | MR | Zbl
[7] Connes A., Sullivan D., Teleman N., “Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes”, Topology, 33 (1994), 663–681 | DOI | MR | Zbl
[8] Fedosov B. V., Golse F., Leichtnam E., Schrohe E., “The noncommutative residue for manifolds with boundary”, J. Funct. Anal., 142 (1996), 1–31 | DOI | MR | Zbl
[9] Gracia-Bondía J. M., Várilly J. C., Figueroa H., Elements of noncommutative geometry, Birkhäuser Advanced Texts, Birkhäuser, Boston, 2001 | MR | Zbl
[10] Graham R., Jenne R., Mason L., Sparling G., “Conformally invariant powers of the Laplacian. I. Existence”, J. London Math. Soc. (2), 46 (1992), 557–565 | DOI | MR | Zbl
[11] Grubb G., “Singular Green operators and their spectral asymptotics”, Duke Math. J., 51 (1984), 477–528 | DOI | MR | Zbl
[12] Guillemin V. W., “A new proof of Weyl's formula on the asymptotic distribution of eigenvalues”, Adv. Math., 55 (1985), 131–160 | DOI | MR | Zbl
[13] Manin Yu. I., “Algebraic aspects of nonlinear differential equations”, J. Sov. Math., 11 (1979), 1–22 | DOI
[14] Paneitz S., A quadratic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds, Preprint, 1983
[15] Polyakov A., “Quantum geometry of bosonic strings”, Phys. Lett. B, 103 (1981), 207–210 | DOI | MR
[16] Schrohe E., “Noncommutative residue, Dixmier's traces, and heat trace expansions on manifolds with boundary”, Geometric aspects of partial differential equations, Contemp. Math., 242, 1999, 161–186 ; math.AP/9911053 | MR | Zbl
[17] Schrohe E., “A short introduction to Boutet de Monvel's calculus”, Approaches to Singular Analysis, eds. J. Gil, D. Grieser and M. Lesch, Birkhäuser, Basel, 2001, 85–116 | MR | Zbl
[18] Ugalde W. J., “Differential forms canonically associated to even-dimensional compact conformal manifolds”, Clifford Algebras. Applications to Mathematics, Physics, and Engineering, Progress in Mathematical Physics, 34, ed. R. Ablamowicz, Birkhäuser, Boston, 2004, 211–225 ; math.DG/0211240 | MR | Zbl
[19] Ugalde W. J., “A construction of critical GJMS operators using Wodzicki's residue”, Comm. Math. Phys., 261 (2006), 771–788 ; math.DG/0403392 | DOI | MR | Zbl
[20] Ugalde W. J., Differential forms and the Wodzicki residue, math.DG/0211361
[21] Wang Y., “Differential forms and the Wodzicki residue for manifolds with boundary”, J. Geom. Phys., 56 (2006), 731–753 ; math.DG/0609062 | DOI | MR | Zbl
[22] Wang Y., “Differential forms and the noncommutative residue for manifolds with boundary in the non-product case”, Lett. Math. Phys., 77 (2006), 41–51 ; math.DG/0609060 | DOI | MR | Zbl
[23] Wodzicki M., “Local invariants of spectral asymmetry”, Invent. Math., 75 (1984), 143–178 | DOI | MR | Zbl