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Table of Contents First Variation Formula Generalized Bernstein Theorem We set the following notations. Suppose $(M^{n+1},\partial M)$ is the ambient manifold we’re interested in. We say $\mathrm{\Sigma }$ is a capillary minimal surface with contact ange $\theta$ if $\mathrm{\Sigma }$ is a minimal surface with boundary $\partial \mathrm{\Sigma }$ and it has contact angle $\theta$ with $\partial M$ along $\partial \mathrm{\Sigma }$.