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Minimizers of the Willmore functional with a small area constraint

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arxiv 1201.1887 v2 pith:4RPNIMYC submitted 2012-01-09 math.DG math.AP

Tobias Lamm , Jan Metzger This is my paper · ORCID
classification math.DGmath.AP
keywords areawillmoreconstraintfunctionalriemanniansmallclassifycompact
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Concentration of Small Hawking Type Surfaces

    math.DG 2019-09 conditional novelty 7.0 of 10

    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.

  2. Minimizers of Generalized Willmore Functionals

    math.DG 2019-09 conditional novelty 6.0 of 10

    A generalized Willmore framework yields existence of area-constrained, and area-volume-constrained, minimizers among haunted bubble trees, with partial regularity for critical points.

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