1 results
Total mean curvature surfaces in the product space
${\mathbb{S}^{n}\times\mathbb{R}}$ and applications
- Part of
-
- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 66 / Issue 2 / May 2023
- Published online by Cambridge University Press:
- 26 April 2023, pp. 346-365
-
- Article
-
- You have access
- HTML
- Export citation
-
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.
