Total mean curvature surfaces in the product space S^n x R and applications
Author
Albujer, Alma L.
Ferreira da Silva, Sylvia
Reis dos Santos, Fábio R.
Publisher
Cambridge University PressDate
2023Subject
ℋ-surfaceProduct space
Minimal surface
Clifford torus
Veronese surface
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The total mean curvature functional for submanifolds into the Riemannian product space S^n × 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 H-surfaces in S^n × R, characterizing the cases where the equality is attained.