N-dimensional area of minimal rotational hypersurfaces in spheres. (September 2015)

• Record Type: Journal Article
• Authors: Perdomo, Oscar M.; Wei, Guoxin
• Is Part Of: Nonlinear analysis. Volume 125(2015)
• Page Start: 241
• Page End: 250
• Publication Date: 2015-09
• Subjects: 53C42 -- 53A10; Rotational hypersurfaces -- Minimal hypersurfaces -- Area; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.05.017
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let M R ( n ) denote the set of compact minimal rotational hypersurfaces in the ( n + 1 ) -dimensional sphere S n + 1 . For any compact hypersurface M ⊂ S n + 1, let us denote by | M | its n -dimensional area. In this paper we show that for any integer n ≥ 2, the set of numbers A n = { | M | : M ∈ M R ( n ) } is a discrete set. We also show that if M ∈ M R ( 3 ), then either | M | = | S 3 |, or | M | = | M 0 ( 3 ) |, or | M | > | M 0 ( 3 ) |, where M 0 ( n ) = S n − 1 ( n − 1 n ) × S 1 ( 1 n ) . Finally, for 2 ≤ n ≤ 100 we show numerically evidence that if M ∈ M R ( n ), then either | M | = | S n |, or | M | = | M 0 ( n ) |, or | M | > 2 | M 0 ( n ) | . We strongly believe that for any M ∈ M R ( n ), either | M | = | S n |, or | M | = | M 0 ( n ) |, or | M | > 2 | M 0 ( n ) | for all n .