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.
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.
Accepted:
Published online:
Joachim Lohkamp 1
@article{CRMATH_2006__343_9_585_0, author = {Joachim Lohkamp}, title = {Positive scalar curvature in $ \mathrm{dim}\ensuremath{\geqslant}8$}, journal = {Comptes Rendus. Math\'ematique}, pages = {585--588}, publisher = {Elsevier}, volume = {343}, number = {9}, year = {2006}, doi = {10.1016/j.crma.2006.09.013}, language = {en}, }
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] The classification of simply connected manifolds of positive scalar curvature, Ann. of Math., Volume 111 (1980), pp. 423-434
[3] 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] 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] On the proof of the positive mass conjecture in general relativity, Comm. Math. Phys., Volume 65 (1979), pp. 45-76
[11] On the structure of manifolds with positive scalar curvature, Manuscripta Math., Volume 28 (1979), pp. 159-183
Cited by Sources:
Comments - Policy