Comptes Rendus
no. 9
Differential Geometry/Calculus of Variations
Positive scalar curvature in dim⩾8
[Courbure scalaire positive en dimension ⩾8]

Présenté par : Marcel Berger

Joachim Lohkamp1
1 Mathematisches Institut, Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany
Comptes Rendus. Mathématique, Volume 343 (2006) no. 9, pp. 585-588.

Nous annonçons une suite des résultats et techniques nouveaux qui permit d'étendre les domaines d'application des hypersurfaces minimaux en géométrie de courbure scalaire. Par exemple, la restriction aux dimensions ⩽7 qui emerge d'un problème analytique subtil en dimensions plus grandes est éliminée complètement.

We announce a first series of new results and techniques extending the scope of applications of minimal hypersurfaces in scalar curvature geometry. For instance, the restriction to dimensions ⩽7 which arises from subtle analytic problems in higher dimensions is entirely removed.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.09.013
Joachim Lohkamp 1

1 Mathematisches Institut, Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany 
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Joachim Lohkamp. Positive scalar curvature in $ \mathrm{dim}⩾8$. Comptes Rendus. Mathématique, Volume 343 (2006) no. 9, pp. 585-588. doi : 10.1016/j.crma.2006.09.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.09.013/

[1] U. Christ, J. Lohkamp, Singular minimal hypersurfaces and scalar curvature, Preprint

[2] M. Gromov; B. Lawson The classification of simply connected manifolds of positive scalar curvature, Ann. of Math., Volume 111 (1980), pp. 423-434

[3] M. Gromov; B. Lawson Spin and scalar curvature in the presence of a fundamental group, Ann. of Math., Volume 111 (1980), pp. 209-230

[4] J. Lohkamp, Inductive analysis on singular minimal hypersurfaces, Preprint

[5] J. Lohkamp, Smoothings of parametric hypersurfaces with obstacles, Preprint

[6] J. Lohkamp, Large manifolds and minimal hypersurfaces, in preparation

[7] J. Lohkamp, The higher dimensional positive mass conjecture I, Preprint

[8] J. Lohkamp, The higher dimensional positive mass conjecture II, in preparation

[9] R. Schoen; S.T. Yau Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature, Ann. of Math., Volume 110 (1979), pp. 127-142

[10] R. Schoen; S.T. Yau On the proof of the positive mass conjecture in general relativity, Comm. Math. Phys., Volume 65 (1979), pp. 45-76

[11] R. Schoen; S.T. Yau On the structure of manifolds with positive scalar curvature, Manuscripta Math., Volume 28 (1979), pp. 159-183

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