[La masse de Gauss–Bonnet–Chern sur des variétés asymptotiquement hyperboliques]
By using the Gauss–Bonnet curvature, we introduce a higher-order mass, the Gauss–Bonnet–Chern mass, for asymptotically hyperbolic manifolds and show that it is a geometric invariant. Moreover, we prove a positive mass theorem for this new mass for asymptotically hyperbolic graphs. Then, we prove the weighted Alexandrov–Fenchel inequalities in the hyperbolic space
En utilisant la courbure de Gauss–Bonnet, on introduit une nouvelle masse dʼordre supérieur – la masse de Gauss–Bonnet–Chern –, sur des variétés asymptotiquement hyperboliques. On montre quʼil sʼagit dʼun invariant géométrique. On démontre également le théorème de masse positive sur des graphes sur lʼespace hyperbolique
Accepté le :
Publié le :
Yuxin Ge 1 ; Guofang Wang 2 ; Jie Wu 2, 3
@article{CRMATH_2014__352_2_147_0, author = {Yuxin Ge and Guofang Wang and Jie Wu}, title = {The {GBC} mass for asymptotically hyperbolic manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {147--151}, publisher = {Elsevier}, volume = {352}, number = {2}, year = {2014}, doi = {10.1016/j.crma.2013.11.019}, language = {en}, }
Yuxin Ge; Guofang Wang; Jie Wu. The GBC mass for asymptotically hyperbolic manifolds. Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 147-151. doi : 10.1016/j.crma.2013.11.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.11.019/
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☆ This project is partly supported by SFB/TR71 “Geometric partial differential equations” of DFG.
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