Existence and uniqueness of smooth solutions are proved for the capillary Christoffel-Minkowski problem, equivalent to a Hessian equation with Robin boundary condition, under a natural sufficient condition.
The capillary Gauss curvature flow
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The capillary Christoffel-Minkowski problem
Existence and uniqueness of smooth solutions are proved for the capillary Christoffel-Minkowski problem, equivalent to a Hessian equation with Robin boundary condition, under a natural sufficient condition.