Time：14:00-15:00, Tuesday, March 10 2026
Venue：E14-212
Host：Jintian Zhu, ITS
Speaker： Yuchen Bi, University of Freiburg
Title：Quantitative rigidity for almost constant mean curvature surfaces in \mathbb{R}^3
Abstract：We prove a quantitative rigidity result for almost constant mean curvature spheres in \mathbb{R}^3. Under a sub--two--sphere Willmore bound and a small L^2 CMC defect, we show that an almost--CMC surface is close to the round sphere, with linear control of the W^{2,2} distance of a conformal parametrization and the L^\infty norm of the conformal factor. An analogous statement holds under an a priori area bound below that of two spheres. The proof relies on a linearized analysis around the sphere, while a previously established qualitative rigidity result provides the initial closeness needed to enter the perturbative regime.
This is joint work with Jie Zhou (Capital Normal University, Beijing).
