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Lamm, Tobias; Metzger, Jan; Schulze, Felix

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

Math. Ann. 350, No. 1, 1-78 (2011).
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.
Reviewer: Eugen Pascu (Montréal)

Cited in 2 Reviews
Cited in 23 Documents

MSC:

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

Keywords:

foliations; assimptotically flat manifold; Wilmore functional; Hawking mass; Euler-Lagrange equation

Software:

Maple
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\textit{T. Lamm} et al., Math. Ann. 350, No. 1, 1--78 (2011; Zbl 1222.53028)
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