All Questions

Let $\Omega$ be an open set in a closed manifold, $(M^n, g)$. We can define the perimeter as $$\text{Per}_g(\Omega) = \sup\bigg\{\int_{\Omega} \text{div}_g(T) dVol_g, \; : \; T \in C^1(M, T M), \quad \...

In the famous paper by D. Fischer-Colbrie "Some rigidity theorems for minimal submanifolds of the sphere", the very first sentence reads: It is well known that the regularity of minimal ...

Let $M$ be an analytic manifold with boundary $\partial M$, equipped with a Riemannian metric $g$, which is also analytic up to and including the boundary. Are there Lojasiewicz–Simon estimates ...

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 ...