We provide a rigidity statement for the equality case of the Heintze–Karcher inequality in substatic manifolds. We apply such a result in the warped product setting to fully remove assumption (H4) in the celebrated Brendle’s characterization of constant mean curvature hypersurfaces in warped products.
The Equality Case in the Substatic Heintze–Karcher Inequality / Borghini, S.; Fogagnolo, M.; Pinamonti, A.. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 248:6(2024). [10.1007/s00205-024-02022-7]
The Equality Case in the Substatic Heintze–Karcher Inequality
Borghini S.;Pinamonti A.
2024
Abstract
We provide a rigidity statement for the equality case of the Heintze–Karcher inequality in substatic manifolds. We apply such a result in the warped product setting to fully remove assumption (H4) in the celebrated Brendle’s characterization of constant mean curvature hypersurfaces in warped products.File in questo prodotto:
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