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{\textendash}Beltrami} operator in a compact manifold}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1231--1265}, publisher = {Elsevier}, volume = {31}, number = {6}, year = {2014}, doi = {10.1016/j.anihpc.2013.09.001}, mrnumber = {3280066}, zbl = {1304.58011}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2013.09.001/} }
TY - JOUR AU - Sicbaldi, Pieralberto TI - Extremal domains of big volume for the first eigenvalue of the Laplace–Beltrami operator in a compact manifold JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 SP - 1231 EP - 1265 VL - 31 IS - 6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2013.09.001/ DO - 10.1016/j.anihpc.2013.09.001 LA - en ID - AIHPC_2014__31_6_1231_0 ER -
%0 Journal Article %A Sicbaldi, Pieralberto %T Extremal domains of big volume for the first eigenvalue of the Laplace–Beltrami operator in a compact manifold %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 1231-1265 %V 31 %N 6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2013.09.001/ %R 10.1016/j.anihpc.2013.09.001 %G en %F 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, Volume 31 (2014) no. 6, pp. 1231-1265. doi : 10.1016/j.anihpc.2013.09.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2013.09.001/
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