A strictly convex capillary hypersurface with prescribed k-th Weingarten curvature exists whenever the prescribed data is symmetric under horizontal reflection.
Minkowski’s and related problems for conv ex surfaces with bound- aries
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Convex capillary hypersurfaces of prescribed curvature problem
A strictly convex capillary hypersurface with prescribed k-th Weingarten curvature exists whenever the prescribed data is symmetric under horizontal reflection.