We prove the existence of new extremal domains for the first eigenvalue of the Laplace–Beltrami operator in some compact Riemannian manifolds of dimension . The volume of such domains is close to the volume of the manifold. If the first eigenfunction of the Laplace–Beltrami operator over the manifold is a nonconstant function, these domains are close to the complement of geodesic balls centered at a nondegenerate critical point of . If is a constant function and , these domains are close to the complement of geodesic balls centered at a nondegenerate critical point of the scalar curvature.
@article{AIHPC_2014__31_6_1231_0, author = {Sicbaldi, Pieralberto}, title = {Extremal domains of big volume for the first eigenvalue of the Laplace--Beltrami operator in a compact manifold}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {31}, year = {2014}, pages = {1231-1265}, doi = {10.1016/j.anihpc.2013.09.001}, mrnumber = {3280066}, zbl = {1304.58011}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2014__31_6_1231_0} }
Sicbaldi, Pieralberto. Extremal domains of big volume for the first eigenvalue of the Laplace–Beltrami operator in a compact manifold. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) pp. 1231-1265. doi : 10.1016/j.anihpc.2013.09.001. http://gdmltest.u-ga.fr/item/AIHPC_2014__31_6_1231_0/
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