On généralise quelques résultats par Goldshtein, Kuzminov et Shvedov sur la cohomologie des cylindres tordus à cohomologie pour . Comme application, on établit des conditions suffisantes pour la non-nullité de la torsion d’une surface de révolution.
We extend some results by Goldshtein, Kuzminov, and Shvedov about the -cohomology of warped cylinders to -cohomology for . As an application, we establish some sufficient conditions for the nontriviality of the -torsion of a surface of revolution.
@article{AMBP_2009__16_2_321_0, author = {Kopylov, Yaroslav}, title = {$L\_{p,q}$-cohomology of warped cylinders}, journal = {Annales math\'ematiques Blaise Pascal}, volume = {16}, year = {2009}, pages = {321-338}, doi = {10.5802/ambp.270}, zbl = {1196.53025}, mrnumber = {2568869}, language = {en}, url = {http://dml.mathdoc.fr/item/AMBP_2009__16_2_321_0} }
Kopylov, Yaroslav. $L_{p,q}$-cohomology of warped cylinders. Annales mathématiques Blaise Pascal, Tome 16 (2009) pp. 321-338. doi : 10.5802/ambp.270. http://gdmltest.u-ga.fr/item/AMBP_2009__16_2_321_0/
[1] Weighted inequalities of Hardy type, Siberian Math. J., Tome 30 (1989) no. 1, pp. 8-16 | Article | MR 995015 | Zbl 0729.42007
[2] On the Hodge theory of Riemannian pseudomanifolds, Geometry of the Laplace Operator, Amer. Math. Soc., Providence (Proc. Sympos. Pure Math.) Tome 36 (1980), pp. 91-146 | MR 573430 | Zbl 0461.58002
[3] Differential forms on Lipschitz manifolds, Siberian Math. J., Tome 23 (1982) no. 2, pp. 151-161 | Article | Zbl 0522.58001
[4] Integration of differential forms of the classes , Siberian Math. J., Tome 23 (1982) no. 5, pp. 640-653 | Article | Zbl 0522.58002
[5] Wolfe’s theorem for differential forms of classes , Siberian Math. J., Tome 24 (1983) no. 5, pp. 672-681 | Article | Zbl 0547.58003
[6] A property of the de Rham regularization operator, Siberian Math. J., Tome 25 (1984) no. 2, pp. 251-257 | Article | Zbl 0602.58002
[7] The integral representation of the integral of a differential form, Functional Analysis and Mathematical Physics, Collect. Sci. Works, Inst. Mat. Sib. Otd. Akad Nauk SSSR, Novosibirsk (1985), pp. 53-87 | Zbl 0583.58002
[8] Normal and compact solvability of linear operators, Siberian Math. J., Tome 30 (1989) no. 5, pp. 704-712 | Article | MR 1025289 | Zbl 0706.47005
[9] -cohomology of warped cylinders, Siberian Math. J., Tome 31 (1990) no. 6, pp. 919-925 | Article | MR 1097955 | Zbl 0732.53029
[10] Reduced -cohomology of warped cylinders, Siberian Math. J., Tome 31 (1990) no. 5, pp. 716-727 | Article | MR 1088912 | Zbl 0722.53034
[11] The -cohomology of SOL, Ann. Fac. Sci. Toulouse Math. (6), Tome 7 (1998) no. 4, pp. 687-698 | Numdam | MR 1693577 | Zbl 0962.53031
[12] Sobolev inequalities for differential forms and -cohomology, J. Geom. Anal., Tome 16 (2006) no. 4, pp. 597-632 | MR 2271946 | Zbl 1105.58008
[13] A conformal de Rham complex (2007) (Preprint arXiv:0711.1286v2. [math.CV])
[14] Distortion of mappings and -cohomology, Math. Z. (2009), pp. 264-279 | Article
[15] -cohomology of Riemannian manifolds with negative curvature, Sobolev spaces in mathematics. II, Springer, New York (Int. Math. Ser. (N. Y.)) Tome 9 (2009), pp. 199-208 | MR 2484626 | Zbl pre05553252
[16] Some properties of the operator of exterior derivation on surfaces of revolution and -cohomology, Complex Geometry of Groups, Amer. Math. Soc., Providence, RI (Contemp. Math.) Tome 240 (1999), pp. 247-257 | MR 1703564 | Zbl 0953.58001
[17] -cohomology and normal solvability, Arch. Math., Tome 89 (2007) no. 1, pp. 87-96 | Article | MR 2322785 | Zbl 1130.58003
[18] Exactness of the cohomology sequence corresponding to a short exact sequence of complexes in a semiabelian category, Siberian Adv. Math., Tome 13 (2003) no. 3, pp. 72-80 | MR 2028407 | Zbl 1046.18010
[19] On normal solvability of the operator of exterior derivation on warped products, Siberian Math. J., Tome 37 (1996) no. 2, pp. 276-287 | Article | MR 1425341 | Zbl 0893.58004
[20] Homological aspects of the theory of Banach complexes, Siberian Math. J., Tome 40 (1999) no. 4, pp. 754-763 | Article | MR 1721681 | Zbl 0939.58001
[21] Sobolev Spaces, Springer-Verlag, New York (1985) | MR 817985 | Zbl 0692.46023
[22] On the Hodge decomposition in (2007) (Preprint arXiv:0710.5414v1 [math.FA])