Existence of integral \(m\)-varifolds minimizing \(\int |A|^p\) and \(\int |H|^p\), \(p>m\), in Riemannian manifolds

DOI10.1007/s00526-012-0588-yzbMath1282.49041arXiv1010.4514OpenAlexW1977559583WikidataQ115387458 ScholiaQ115387458MaRDI QIDQ2636885

Andrea Mondino

Publication date: 18 February 2014

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.4514

zbMATH Keywords

minimizersRiemannian manifoldsintegral \(m\)-varifolds

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20) Variational problems in infinite-dimensional spaces (58E99)

Related Items (10)

Uniform regularity results for critical and subcritical surface energies ⋮ Some geometric inequalities for varifolds on Riemannian manifolds based on monotonicity identities ⋮ Weak and approximate curvatures of a measure: a varifold perspective ⋮ A convergence result for the gradient flow of \(\int|A|^2\) in Riemannian manifolds ⋮ Stationary surfaces with boundaries ⋮ Integral decompositions of varifolds ⋮ Two-dimensional curvature functionals with superquadratic growth ⋮ Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below ⋮ Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds ⋮ Immersions with bounded second fundamental form

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