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Some remarks on singular capillary cones with free boundary
We study singular minimizing capillary cones with free boundary. We provide a stability criterion $à$ Jerison-Savin and use it to prove that a minimizing capillary cone is flat when its free boundary mean curvature is non-negative and $n\leq 4$, or non-positive and $n\leq 6$. We also show that min
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