For small area, minimizers of Hawking type functionals are embedded spheres, and small concentrating sequences for the Hawking energy are shown to accumulate only at critical points of Sc + (3/5)trK² + (1/5)|K|².
Minimizers of the Willmore functional with a small area constraint
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abstract
We show the existence of a smooth spherical surface minimizing the Willmore functional subject to an area constraint in a compact Riemannian three-manifold, provided the area is small enough. Moreover, we classify complete surfaces of Willmore type with positive mean curvature in Riemannian three-manifolds.
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Concentration of Small Hawking Type Surfaces
For small area, minimizers of Hawking type functionals are embedded spheres, and small concentrating sequences for the Hawking energy are shown to accumulate only at critical points of Sc + (3/5)trK² + (1/5)|K|².