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In this paper, we prove the quantitative version of the Alexandrov theorem for capillary hypersurfaces in the half-space. The proof is based on the quantitative analysis of the Montiel-Ros-type argument, carried out in the joint works with Wang-Xia {JWXZ22-B,JWXZ23}. As by-products, we obtain new Michael-Simon-type inequality and Topping-type inequality for capillary hypersurfaces in the half-space.
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Jia et al. (2024) studied this question.
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