| Autor: |
de Lima, R. F., Elbert, M. F., Nelli, B. |
| Zdroj: |
Mathematische Zeitschrift; Feb2025, Vol. 309 Issue 2, p1-20, 20p |
| Abstrakt: |
We approach the one-parameter family of rotational constant mean curvature (CMC) spheres of H n × R and S n × R focusing on their stability and isoperimetry properties. We prove that all rotational CMC spheres of H n × R are stable, and that the ones in S n × R with sufficiently small (resp. large) mean curvature are unstable (resp. stable). We also show that there exists a one-parameter family of stable CMC rotational spheres in S n × R which are not isoperimetric (i.e., they do not bound isoperimetric regions). We establish the uniqueness of the regions enclosed by the rotational CMC spheres of H n × R as solutions to the isoperimetric problem, filling in a gap in the original proof given by Hsiang and Hsiang. We establish, as well, a sharp upper bound for the volume of the spherical regions of S n × R which are unique solutions to the isoperimetric problem. In essence, all these results come from the fact that the rotational CMC spheres of H n × R , and those of S n × R with sufficiently large mean curvature, are nested. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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