5 problems

A properly embedded minimal surface of finite topology is a properly embedded minimal surface in $R^3$ with finite topological type; an end is an end of the surface, and the total…

Let $\Gamma$ be a closed surface immersed in a $\operatorname{CAT}^3(0)$ manifold, and let $\widetilde{\mathcal{G}}(\Gamma)$ denote its total absolute Gaussian curvature. If $g$ is…

Let $\Gamma'$ be a smoothly embedded, simple closed curve in $\mathbf{R}^3$ that bounds a smooth, oriented minimal surface which is not a disk. The theorem in question currently gi…

Non-algebraic stationary surface conjecture. There does not exist any complete, non-algebraic stationary surface immersed in $\mathbb{R}^4_1$ with finite total Gaussian curvature

Let $\Gamma$ be a graph in $\mathbb{R}^3$ homeomorphic to a circle with two disjoint, parallel chords, and let $\mathcal{N}(\Gamma)$ denote its total curvature. Convexity conjectur…