中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
偏微分方程研讨班
Speaker: 周杰（首都师范大学）
Inviter: 张翼
Language: Chinese
Title: Linear bi-Lipschitz Quantitative Rigidity for L^2 Almost-CMC Surfaces
Time & Venue: 2026年7月23日（星期四） 10:00-11:00 思源楼S813
Abstract: In this presentation, we talk about the quantitative rigidity result for almost constant mean curvature spheres in R^3. Under a sub–two–sphere Willmore bound and a small L^2–CMC defect assumption, we show that an almost–CMC surface is close to the round sphere, with linear control of the W^{2,2} distance of the parametrization and the L^∞ norm of the conformal factor. An analogous statement holds under an a priori area bound below that of two spheres. This quantitative rigidity relies on a linearized analysis around the sphere. A previously established qualitative rigidity result provides the initial closeness required to enter the perturbative regime. The estimate further extends to integral 2–varifolds of unit density using known regularity and density results. This is a joint work with Yuchen Bi at University of Freiburg.
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