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Total mean curvature surfaces in the product space 
${\mathbb{S}^{n}\times\mathbb{R}}$ and applications
Published online by Cambridge University Press: 26 April 2023
Abstract
The total mean curvature functional for submanifolds into the Riemannian product space 
$\mathbb{S}^n\times\mathbb{R}$ is considered and its first variational formula is presented. Later on, two second-order differential operators are defined and a nice integral inequality relating both of them is proved. Finally, we prove our main result: an integral inequality for closed stationary 
$\mathcal{H}$-surfaces in 
$\mathbb{S}^n\times\mathbb{R}$, characterizing the cases where the equality is attained.
MSC classification
- Type
- Research Article
- Information
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.
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