4 problems

Let $f_{+}$ and $f_{-}$ be non-congruent conformal immersions of a compact oriented surface into Euclidean $3$-space that induce the same metric and have the same mean curvature: ……

Let $(M,g)$ be a closed and oriented Riemannian surface, let $H$ be a function on $(M,g)$, and let ${\cal F}$ be a regular homotopy class of immersions of $M$ into $\mathbb{R}^3$.…

Let $(M,g)$ be a closed oriented Riemannian surface, and let $H:M\to\mathbb{R}$ be an arbitrary non-constant function. Two isometric immersions are congruent if they differ by a ri…

Let $\Sigma^2$ be a closed surface of genus at least $1$, let $M^3$ be a $3$-manifold, and let $\phi\colon \Sigma^2\to M^3$ be a two-sided immersion. Call $\phi$ compressible if th…