Around heat decay on forms and relations of nilpotent Lie groups

 Access to full text

 Full (PDF)

1. [1] M.F. Atiyah. Elliptic operators, discrete groups and von Neumann algebras. Astérisque, 32-33 ( 1976), 43-72. Zbl0323.58015MR420729
2. [2] R. Brooks. The fundamental group and the spectrum of the Laplacian. Comment. Math. Helu, 56 ( 1981), 581-598. Zbl0495.58029MR656213
3. [3] James A.Carlson and Domingo Toledo. Quadratic présentations and nilpotent Kahler groups. J. Geom. Anal..5(3):359-377, 1995. Zbl0835.57014MR1360825
4. [4] William Casselman and M. Scott Osborne. The n-cohomology of representations with an infinitesimal character. Compositio Math.,31 (2):219-227, 1975. Zbl0343.17006MR396704
5. [5] Shirnping Chen. Examples of n-step nilpotent 1-formal 1-minimal models. C. R.Acad. Sci. Paris Sér. I Math., 321(2):223-228, 1995. Zbl0881.55011MR1345452
6. [6] Michael Christ, Daryl Geiler, Pawel Gtowacki, and Larry Polin. Pseudodifferential operators on groups with dilations. DukeMath. J., 68(l):31-65, 1992. Zbl0764.35120
7. [7] Michael Cowling, Anthony H. Dooley Adam Koranyi, and Fulvio Ricci, H-type groups and Iwasawa decompositions. Adv. Math., 87(1):1-41, 1991. Zbl0761.22010
8. [8] L. Corwin and E. P. Greenleaf. Representations of nilpotent Lie groups and their applications. Part I. Cambridge University Press, Cambridge, 1990. Zbl0704.22007
9. [9] Ch. Deninger and W. Singhof. On the cohomology of nilpotent Lie algebras. Bull. Soc. Math.France, 116(1):3-14, 1988. Zbl0653.17006
10. [10] J. Dixmier. Cohomologie des algèbres de Lie nilpotentes. Acta Sci. Math., 16:246-250. 1955. Zbl0066.02403
11. [11] G. B. Folland. Subelliptic estimates and function spaces on nilpotent Lie groups. Ark. Mat., 13(2): 161-207, 1975. Zbl0312.35026MR494315
12. [12] Phillip A. Griffiths and John W. Morgan, Rational homotopy theory and differential forms. Birkhäuser Boston, Mass., 1981. Zbl0474.55001MR641551
13. [13] M. Gromov. Carnot-Carathéodory spaces seen from within. In A. Bellaïche and J.-J. Risler, editors, Sub-Riemannian Geometry, volume 144 of Progress in Math, pages 79-323. Birkhäuser 1996. Zbl0864.53025MR1421823
14. [14] M. Gromov and M.A. Shubin. Von Neumann spectra near zero. Geometrie and Functional Analysis, 1 (4) ( 1991), 375-404. Zbl0751.58039MR1132295
15. [15] M. Gromov and M.A. Shubin. Near-cohomology of Hilbert complexes and topology of non-simply connected manifolds. In Méthodes semi-classiques. Astérisque, 210 ( 1992), 283-294. Zbl0797.57016MR1221363
16. [16] B. Helffer and J. Nourrigat. Caractérisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe de Lie nilpotent gradué. Comm. Partial Differential Equations,4 (8):899-958, 1979. Zbl0423.35040MR537467
17. [17] Bernard Helffer and Jean Nourrigat. Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs. Birkhäuser Boston Inc., Boston, MA, 1985. Zbl0568.35003MR897103
18. [18] Dale Husemoller. Fibre bundies. Springer-Verlag, New York, third edition, 1994. Zbl0307.55015MR1249482
19. [19] Aroldo Kaplan. On the geometry of groups of Heisenberg type. Bull. London Math. Soc, 15(l):35-42, 1983. Zbl0521.53048MR686346
20. [20] John Lott. Heat kernels on covering spaces and topological invariants. J. Differential Geom., 35(2):471-510, 1992. Zbl0770.58040MR1158345
21. [21] P. Pansu. Introduction to L2 Betti numbers. In Riemannian geometry (Waterloo, ON, 1993), pages 53-86. Amer. Math. Soc, Providence, RI, 1996. Zbl0848.53025MR1377309
22. [22] Linda Preiss Rothschild and E. M. Stein. Hypoelliptic differential operators and nilpotent groups. Acta Malh., 137(3-4) :247-320, 1976. Zbl0346.35030MR436223
23. [23] M. Reed and B. Simon. Methods of Modem Mathematical Physics, volumes 1and 2 : Functional Analysis. Academie Press, 1972. Zbl0242.46001
24. [24] M. Rumin. Un complexe de formes différentielles sur les variétés de contact. C. R.Acad. Sci. ParisSér. I Math., 310(6):401-404, 1990. Zbl0694.57010MR1046521
25. [25] M. Rumin. Differential geometry on C-C spaces and application to the Novikov-Shubin numbers of nilpotent Lie groups. C. R. Acad. Sci. Paris Sér. I Math., 329(11):985-990, 1999. Zbl0982.53029MR1733906
26. [26] Simon Salamon. Riemannian geometry and holonomy groups. Longman Scientific & Technical, Harlow, 1989. Zbl0685.53001MR1004008
27. [27] N. Th. Varopoulos, L. Saloff-Coste, and T. Coulhon. Analysis and geometry on groups. Cambridge University Press, Cambridge, 1992. Zbl1179.22009MR1218884

1. Annalisa Baldi, Bruno Franchi, Some Remarks on Vector Potentials for Maxwell's Equations in Space-Time Carnot Groups
2. Pascal Auscher, Thierry Coulhon, Xuan Thinh Duong, Steve Hofmann, Riesz transform on manifolds and heat kernel regularity