scholarly journals L 2 harmonic 2-forms on minimal hypersurfaces in spheres

2018 ◽  
Vol 56 ◽  
pp. 202-210 ◽  
Author(s):  
Wenzhen Gan ◽  
Peng Zhu ◽  
Shouwen Fang
Keyword(s):  
Minimal Hypersurfaces ◽  
Hypersurfaces In Spheres

scholarly journals Minimal hypersurfaces with small first eigenvalue in manifolds of positive Ricci curvature

2016 ◽  
Vol 09 (03) ◽  
pp. 505-532
Author(s):  
Jonathan J. Zhu
Keyword(s):  
Lower Bound ◽  
Ricci Curvature ◽  
First Eigenvalue ◽  
Positive Ricci Curvature ◽  
Minimal Hypersurfaces ◽  
The First Eigenvalue ◽  
Geometric Data ◽  
Laplace Eigenvalue ◽  
Hypersurfaces In Spheres

In this paper we exhibit deformations of the hemisphere [Formula: see text], [Formula: see text], for which the ambient Ricci curvature lower bound [Formula: see text] and the minimality of the boundary are preserved, but the first Laplace eigenvalue of the boundary decreases. The existence of these metrics suggests that any resolution of Yau’s conjecture on the first eigenvalue of minimal hypersurfaces in spheres would likely need to consider more geometric data than a Ricci curvature lower bound.

scholarly journals Estimate for index of closed minimal hypersurfaces in spheres

2009 ◽  
Vol 32 (3) ◽  
pp. 442-449 ◽  
Author(s):  
Abdênago Alves de Barros ◽  
Paulo Alexandre Araújo Sousa
Keyword(s):  
Minimal Hypersurfaces ◽  
Hypersurfaces In Spheres

The scalar curvature of minimal hypersurfaces in spheres

1983 ◽  
Vol 266 (1) ◽  
pp. 105-113 ◽  
Author(s):  
Chia-Kuei Peng ◽  
Chuu-Lian Terng
Keyword(s):  
Scalar Curvature ◽  
Minimal Hypersurfaces ◽  
Hypersurfaces In Spheres

O(m) � O(n)-Invariant Minimal Hypersurfaces in $\mathbb{R}$ m+n

2005 ◽  
Vol 27 (2) ◽  
pp. 179-199 ◽  
Author(s):  
Hil�rio Alencar ◽  
Abd�nago Barros ◽  
Oscar Palmas ◽  
J. Guadalupe Reyes ◽  
Walcy Santos
Keyword(s):  
Minimal Hypersurfaces

POLAR HYPERSURFACES IN SPHERES

1999 ◽  
Author(s):  
F. BRITO ◽  
H. L. LIU ◽  
V. I. OLIKER ◽  
U. SIMON ◽  
C. P. WANG
Keyword(s):  
Hypersurfaces In Spheres
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