A half-space type property in the Euclidean sphere
Archivum mathematicum, Tome 58 (2022) no. 1, pp. 49-63.
Voir la notice de l'article dans Czech Digital Mathematics Library
We study the notion of strong -stability for the context of closed hypersurfaces ( ) with constant -th mean curvature immersed into the Euclidean sphere , where . In this setting, under a suitable restriction on the -th mean curvature , we establish that there are no -strongly stable closed hypersurfaces immersed in a certain region of , a region that is determined by a totally umbilical sphere of . We also provide a rigidity result for such hypersurfaces.
DOI :
10.5817/AM2022-1-49
Classification :
53C21, 53C42
Mots-clés : Euclidean sphere; closed hypersurfaces; -th mean curvature; strong -stability; geodesic spheres; upper (lower) domain enclosed by a geodesic sphere
Mots-clés : Euclidean sphere; closed hypersurfaces;
@article{10_5817_AM2022_1_49, author = {Vel\'asquez, Marco Antonio L\'azaro}, title = {A half-space type property in the {Euclidean} sphere}, journal = {Archivum mathematicum}, pages = {49--63}, publisher = {mathdoc}, volume = {58}, number = {1}, year = {2022}, doi = {10.5817/AM2022-1-49}, mrnumber = {4412967}, zbl = {07511507}, language = {en}, url = {https://geodesic-test.mathdoc.fr/articles/10.5817/AM2022-1-49/} }
TY - JOUR AU - Velásquez, Marco Antonio Lázaro TI - A half-space type property in the Euclidean sphere JO - Archivum mathematicum PY - 2022 SP - 49 EP - 63 VL - 58 IS - 1 PB - mathdoc UR - https://geodesic-test.mathdoc.fr/articles/10.5817/AM2022-1-49/ DO - 10.5817/AM2022-1-49 LA - en ID - 10_5817_AM2022_1_49 ER -
Velásquez, Marco Antonio Lázaro. A half-space type property in the Euclidean sphere. Archivum mathematicum, Tome 58 (2022) no. 1, pp. 49-63. doi : 10.5817/AM2022-1-49. https://geodesic-test.mathdoc.fr/articles/10.5817/AM2022-1-49/
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