All Questions

Does there exist a closed, bounded surface $S$ embedded in $\mathbb{R}^3$ that has a geodesic $\gamma$ that spirals around a point $x$, getting closer and closer, but never reaching $x$? Here I ...

Let $S$ be the surface of a convex body embedded in $\mathbb{R}^3$. For me $S$ is a convex polyhedron, but I am happy to view $S$ as a smooth body with positive Gaussian curvature at each point, or ...

Let $\gamma$ be a smooth, closed, unknotted curve embedded in $\mathbb{R}^3$. Q. Does there always exist a smooth, embedded, genus-zero surface $S \subset \mathbb{R}^3$ such that $\gamma$ is a (...