发表机构
Metropolitan State University of Denver; University of California, Santa Cruz（丹佛大都会州立大学; 加州大学圣克鲁兹分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对González和Qing引入的分数Yamabe泛函，通过Lyapunov-Schmidt约化结合分数共形拉普拉斯算子延拓刻画，证明其极小化子的定量稳定性，并得到相关延拓泛函的类似估计。
AI 中文摘要
我们研究由González和Qing引入的分数Yamabe泛函的定量稳定性，其极小化子对应具有常数分数曲率的共形度量。我们证明分数Yamabe泛函的亏格以适当的幂次控制到极小化子集合的距离。我们的方法基于非局部泛函的Lyapunov-Schmidt约化，结合分数共形拉普拉斯算子的延拓刻画，为局部分析提供所需的正则性理论。作为结果，我们还得到相关延拓泛函的类似定量稳定性估计。
英文摘要
We study quantitative stability for the fractional Yamabe functional introduced by González and Qing. Its minimizers correspond to conformal metrics with constant fractional curvature. We prove that the deficit of the fractional Yamabe functional controls, with a suitable power, the distance to the set of minimizers. Our approach is based on a Lyapunov--Schmidt reduction for the nonlocal functional, together with the extension characterization of the fractional conformal Laplacian, which provides the regularity theory needed for the local analysis. As a consequence, we also obtain an analogous quantitative stability estimate for the associated extension functional.
Comments29 pages
