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Let $(\Sigma,g)$ be a compact surface without boundary. Given $\epsilon > 0$, the $\epsilon$-Allen-Cahn equation is the semilinear elliptic PDE $\epsilon \Delta_g u - \epsilon^{-1} W'(u) = 0$, with ...

The definition of generalized mean curvature on $C^1$ hypersurfaces is given as follows: Let $M$ be a closed orientable $C^1$ hypersurface in $\mathbb{R}^{n+1}$ and $\mu$ be the $n$-dimensional ...