Stefano Borghini, Mattia Fogagnolo, Andrea Pinamonti
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The Equality Case in the Substatic Heintze–Karcher Inequality
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.
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The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.
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