Willmore spheres in compact Riemannian manifolds

DOI10.1016/j.aim.2012.09.014zbMath1294.30046arXiv1203.5501OpenAlexW2951564519WikidataQ115362068 ScholiaQ115362068MaRDI QIDQ1929210

Tristan Rivière, Andrea Mondino

Publication date: 7 January 2013

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.5501

zbMATH Keywords

minimal surfacesconformal differential geometryelliptic regularity theorygeometric PDEoptimal surfacesweak immersions

Mathematics Subject Classification ID

Variational principles in infinite-dimensional spaces (58E30) Variational methods for elliptic systems (35J50) Optimization of shapes other than minimal surfaces (49Q10) Extremal problems for conformal and quasiconformal mappings, variational methods (30C70) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15) Variational methods for higher-order elliptic equations (35J35) PDEs on manifolds (35R01) Higher-order elliptic systems (35J48)

Related Items (19)

Uniform regularity results for critical and subcritical surface energies ⋮ Noether's theorem and the Willmore functional ⋮ The Classification of Branched Willmore Spheres in the 3-Sphere and the 4-Sphere ⋮ A convergence result for the gradient flow of \(\int|A|^2\) in Riemannian manifolds ⋮ Global Conformal Invariants of Submanifolds ⋮ Minimizers of the Willmore functional with a small area constraint ⋮ Embedded surfaces of arbitrary genus minimizing the Willmore energy under isoperimetric constraint ⋮ A resolution of the Poisson problem for elastic plates ⋮ A viscosity method in the min-max theory of minimal surfaces ⋮ Phase field models for thin elastic structures with topological constraint ⋮ The Willmore functional of surfaces ⋮ Local foliation of manifolds by surfaces of Willmore-type ⋮ Energy quantization of Willmore surfaces at the boundary of the moduli space ⋮ Candidates for non-rectangular constrained Willmore minimizers ⋮ First explicit constrained Willmore minimizers of non-rectangular conformal class ⋮ Critical weak immersed surfaces within sub-manifolds of the Teichmüller space ⋮ On the minimizers of curvature functionals in asymptotically flat manifolds ⋮ An Hélein’s type convergence theorem for conformal immersions from 𝕊² to manifold ⋮ Concentration of small Hawking type surfaces

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