Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds

DOI10.1016/J.ANIHPC.2013.07.002zbMath1300.53042arXiv1201.2165OpenAlexW3098432451MaRDI QIDQ457834

Johannes Schygulla, Andrea Mondino

Publication date: 29 September 2014

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.2165

zbMATH Keywords

general relativityWillmore functionalgeometric measure theory\(L^2\) second fundamental formdirect methods in the calculus of variations

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Variational problems in infinite-dimensional spaces (58E99)

Related Items (4)

Some rigidity results for the Hawking mass and a lower bound for the Bartnik capacity ⋮ Solutions of spinorial Yamabe-type problems on 𝑆^{𝑚}: Perturbations and applications ⋮ Lower semicontinuity for the Helfrich problem ⋮ On the minimizers of curvature functionals in asymptotically flat manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Foliations of asymptotically flat manifolds by surfaces of Willmore type
• Some results about the existence of critical points for the Willmore functional
• Analysis aspects of Willmore surfaces
• Existence and uniqueness of constant mean curvature foliation of asymptotically hyperbolic 3-manifolds
• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• On the proof of the positive mass conjecture in general relativity
• Removability of point singularities of Willmore surfaces
• Existence of surfaces minimizing the Willmore functional
• Willmore minimizers with prescribed isoperimetric ratio
• Small Surfaces of Willmore Type in Riemannian Manifolds
• The Yamabe problem

This page was built for publication: Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds