The Conformal Willmore Functional: A Perturbative Approach

@article{Mondino2013TheCW,
  title={The Conformal Willmore Functional: A Perturbative Approach},
  author={Andrea Mondino},
  journal={Journal of Geometric Analysis},
  year={2013},
  volume={23},
  pages={764-811}
}
The conformal Willmore functional (which is conformal invariant in general Riemannian manifolds (M,g)) is studied with a perturbative method: the Lyapunov–Schmidt reduction. Existence of critical points is shown in ambient manifolds (ℝ3,gϵ)—where gϵ is a metric close and asymptotic to the Euclidean one. With the same technique a non-existence result is proved in general Riemannian manifolds (M,g) of dimension three. 
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