Foliations of asymptotically flat manifolds by surfaces of Willmore type. (English) Zbl 1222.53028

In the frame of the study of the foliations of asymptotically flat manifolds, the authors are interested in constructing embedded spheres \(\Sigma\) in a Riemannian manifold \((M,g)\) which satisfy the equation: \(- \Delta H -H |\AA|^{2} - ^{M}\)Rc\((\nu, \nu)H = \lambda H\), where \(H\) is the mean curvature of \(\Sigma\), \(\AA = A- \frac{1}{2}H \gamma\) (\(\gamma\) is the induced metric on \( \Sigma\)), \(^{M}\)Rc is the Ricci curvature of \(M\) and \(\Delta \) is the Laplace-Beltrami operator on \( \Sigma\). The authors argue that the above equation is the most natural equation to consider when defining a geometric center of the Hawking mass. The preliminaries necessary for the understanding of their interesting results, discussions and other points of view on the subject are also presented.


53C12 Foliations (differential geometric aspects)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C80 Applications of global differential geometry to the sciences
83C99 General relativity


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