Huisken-Yau-type uniqueness for area-constrained Willmore spheres

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Equations of motion in general relativity and gravitational theory (83C10)

Cites Work

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Constant mean curvature surfaces in warped product manifolds
Foliations of asymptotically flat manifolds by surfaces of Willmore type
Foliations by stable spheres with constant mean curvature for isolated systems with general asymptotics
Optimal rigidity estimates for nearly umbilical surfaces
On the radius pinching estimate and uniqueness of the CMC foliation in asymptotically flat 3-manifolds
The inverse mean curvature flow and the Riemannian Penrose inequality
Elliptic partial differential equations of second order
The Willmore flow with small initial energy.
Discrete and continuous Green energy on compact manifolds
Existence of surfaces minimizing the Willmore functional
Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature
The area preserving Willmore flow and local maximizers of the Hawking mass in asymptotically Schwarzschild manifolds
Global uniqueness of large stable CMC spheres in asymptotically flat Riemannian \(3\)-manifolds
The Willmore center of mass of initial data sets
On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds
Isoperimetry, Scalar Curvature, and Mass in Asymptotically Flat Riemannian 3‐Manifolds
Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds I: minimization
Scalar curvature deformation and a gluing construction for the Einstein constraint equations

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