A remark on the non-compactness of 𝑊^{2,𝑑}-immersions of 𝑑-dimensional hypersurfaces

DOI10.1090/proc/14710zbMath1436.53007arXiv1807.00360OpenAlexW2963937644MaRDI QIDQ5221366

Siran Li

Publication date: 25 March 2020

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.00360

zbMATH Keywords

second fundamental formhypersurfacecompactnessGauss mapimmersionsfiniteness theoremschord-arc surfacebounded mean oscillations (BMO)

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Spaces of embeddings and immersions (58D10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Immersions in differential topology (57R42)

Cites Work

• Unnamed Item
• The div-curl lemma for sequences whose divergence and curl are compact in \(W^{-1,1}\)
• Chord-arc surfaces with small constant. I
• Chord-arc surfaces with small constant. II: Good parametrizations
• A compactness theorem for surfaces with \(L_ p\)-bounded second fundamental form
• Surfaces with generalized second fundamental form in \(L^ 2\) are Lipschitz manifolds
• Global weak rigidity of the Gauss-Codazzi-Ricci equations and isometric immersions of Riemannian manifolds with lower regularity
• Immersions with bounded second fundamental form
• Conservation laws for conformally invariant variational problems
• Immersions with bounded curvature
• Hypersurfaces in R n Whose Unit Normal has Small BMO Norm
• Finiteness Theorems for Riemannian Manifolds

This page was built for publication: A remark on the non-compactness of 𝑊^{2,𝑑}-immersions of 𝑑-dimensional hypersurfaces