Let (M,g) be a three-dimensional Riemannian manifold. The goal of the paper is to show that if P0∈M is a nondegenerate critical point of the scalar curvature, then a neighborhood of P0 is foliated by area-constrained Willmore spheres. Such a foliation is unique among foliations by area-constrained Willmore spheres having Willmore energy less than 32π⁠; moreover, it is regular in the sense that a suitable rescaling smoothly converges to a round sphere in the Euclidean three-dimensional space. We also establish generic multiplicity of foliations and the 1st multiplicity result for area-constrained Willmore spheres with prescribed (small) area in a closed Riemannian manifold. The topic has strict links with the Hawking mass.

中文翻译：

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标量曲率的非退化临界点附近受面积约束的 Willmore 球的叶面化

令 (M,g) 是一个三维黎曼流形。该论文的目的是表明，如果 P0∈M 是标量曲率的非退化临界点，那么 P0 的邻域由面积约束的 Willmore 球面组成。这种叶理在由具有小于 32π 的 Willmore 能量的面积受限的 Willmore 球的叶理中是独一无二的。此外，在欧几里得三维空间中适当的重新缩放平滑地收敛到圆球的意义上，它是有规律的。我们还为在封闭黎曼流形中具有指定（小）面积的面积约束 Willmore 球体建立了一般的多重性和第一多重性结果。这个话题与霍金质量有着严格的联系。