Refined Kato inequalities in riemannian geometry
Herzlich, Marc
Journées équations aux dérivées partielles, (2000), p. 1-11 / Harvested from Numdam

We describe the recent joint work of the author with David M. J. Calderbank and Paul Gauduchon on refined Kato inequalities for sections of vector bundles living in the kernel of natural first-order elliptic operators.

Publié le : 2000-01-01
@article{JEDP_2000____A6_0,
     author = {Herzlich, Marc},
     title = {Refined Kato inequalities in riemannian geometry},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2000},
     pages = {1-11},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_2000____A6_0}
}
Herzlich, Marc. Refined Kato inequalities in riemannian geometry. Journées équations aux dérivées partielles,  (2000), pp. 1-11. http://gdmltest.u-ga.fr/item/JEDP_2000____A6_0/

[1] S. Bando, A. Kasue and H. Nakajima, On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth, Invent. Math. 97 (1989), 313-349. | MR 90c:53098 | Zbl 0682.53045

[2] P. Bérard, From vanishing theorems to estimating theorems : the Bochner technique revisited, Bull. Amer. Math. Soc. 19 (1988), 371-406. | MR 89i:58152 | Zbl 0662.53037

[3] J. P. Bourguignon, The magic of Weitzenböck formulas, in Variational methods (Paris, 1988), H. Brezis, J. M. Coron and I. Ekeland eds, PNLDE vol. 4, Birkhäuser, Zürich, 1990. | Zbl 0774.35003

[4] T. Branson, Stein-Weiss operators and ellipticity, J. Funct. Anal. 151 (1997), 334-383. | MR 99b:58219 | Zbl 0904.58054

[5] T. Branson, Kato constants in Riemannian geometry, Preprint (1999), to appear in Math. Res. Lett. | Zbl 1039.53033

[6] D. M. J. Calderbank, P. Gauduchon, and M. Herzlich, Refined Kato inequalities and conformal weights in Riemannian geometry, J. Funct. Anal. 173 (2000), 214-255. | MR 2001f:58046 | Zbl 0960.58010

[7] D. M. J. Calderbank, P. Gauduchon, and M. Herzlich, On the Kato inequality in Riemannian Geometry, to appear in Analyse harmonique et analyse sur les variétés, Proc. of the Luminy conf., 1-6 June 1999 (J. P. Bourguignon and O. Hijazi, eds.).

[8] W. Fulton and J. Harris, Representation Theory - A First Course, Grad. Text. Math. vol. 129, Springer, 1991. | MR 93a:20069 | Zbl 0744.22001

[9] P. Gauduchon, Structures de Weyl et théorèmes d'annulation sur une variété conforme autoduale, Ann. Sc. Norm. Sup. Pisa 18 (1991), 563-629. | Numdam | MR 93d:32046 | Zbl 0763.53034

[10] H. Hess, R. Schrader and D. Uhlenbrock, Kato's inequality and the spectral distribution of Laplacians on compact Riemannian manifolds, J. Diff. Geom. 15 (1980), 27-38. | MR 82g:58090 | Zbl 0442.58032

[11] J. Råde, Decay estimates for Yang-Mills fields : two new proofs, Global analysis in modern mathematics (Orono, 1991, Waltham, 1992), Publish or Perish, Houston, 1993, pp. 91-105. | MR 95g:53030 | Zbl 1049.53505

[12] R. Schoen, L. Simon and S. T. Yau, Curvature estimates for minimal hypersurfaces, Acta Math. 134 (1975), 275-288. | MR 54 #11243 | Zbl 0323.53039

[13] K. Uhlenbeck, Removable singularities for Yang-Mills fields, Commun. Math. Phys. 83 (1982), 11-30. | MR 83e:53034 | Zbl 0491.58032