A Heintze-Karcher type inequality for hypersurfaces with capillary boundary
Abstract
In this paper, we establish a Heintze-Karcher type inequality for hypersurfaces with capillary boundary of contact angle θ∈ (0,π2) in a half space or a half ball, by using solution to a mixed boundary value problem in Reilly type formula. Consequently, we give a new proof of Alexandrov type theorem for embedded capillary constant mean curvature hypersurfaces with contact angle θ∈ (0,π2) in a half space or a half ball.
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