Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds. (English) Zbl 1300.53042
The authors focus on minimization of curvature functionals in three-dimensional Riemannian manifolds when the ambient space is non-compact. Specifically, they study the minimizers of the Willmore functional among immersed spheres in the three-dimensional Euclidean space. Then they deal with the minimization of related curvature functionals in non-compact three-dimensional Riemannian manifolds. Applications to general relativity are discussed.
Reviewer: Dumitru Motreanu (Perpignan)
MSC:
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 58E99 | Variational problems in infinite-dimensional spaces |
| 35J60 | Nonlinear elliptic equations |
Keywords:
\(L^2\) second fundamental form; Willmore functional; direct methods in the calculus of variations; geometric measure theory; general relativityReferences:
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