Caffarelli对数凹摄动定理的刚性和稳定性
Rigidity and stability of Caffarelli's log-concave perturbation theorem
摘要：
本文建立了Caffarelli对数凹摄动定理的刚性和稳定性结果。作为应用，我们证明了如果一个1-log凹测度与高斯测度具有几乎相同的Poincaré常数，那么它几乎分裂出一个高斯因子。
英文摘要：
In this note we establish some rigidity and stability results for Caffarelli's log-concave perturbation theorem. As an application we show that if a 1-log-concave measure has almost the same Poincaré constant as the Gaussian measure, then it almost splits off a Gaussian factor.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
