arXiv subjects
Publications and source records attributed to Hunter Stufflebeam.
We prove a conjecture of Marques-Neves in arXiv:2103.10093, and several alternative formulations thereof, about the stability of the min-max width of three-spheres under the additional assumption of rotational symmetry. We can moreover extend our results to all dimensions $n\geqslant 3$.
We prove that strictly convex 2-spheres, all of whose simple closed geodesics are close in length to 2{\pi}, are C^0 Cheeger-Gromov close to the round sphere.
We prove that topological disks with positive curvature and strictly convex boundary of large length are close to round spherical caps of constant boundary curvature in the Gromov-Hausdorff sense. This proves stability for a theorem of F. Hang and X. Wang, and can be viewed as an affirmative answer to a convex stability version of the Min-Oo Conjecture in dimension two. As an intermediate step, we obtain a compactness result for a Liouville-type PDE problem.