Immersions with bounded second fundamental form

DOI10.1007/s12220-014-9472-7zbMath1318.53060arXiv1201.4562OpenAlexW2095251338MaRDI QIDQ2347953

Patrick Breuning

Publication date: 10 June 2015

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.4562

zbMATH Keywords

second fundamental formcompactnessimmersionsbounded curvaturecompact and noncompact manifolds

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Local submanifolds (53B25)

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Cites Work

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• A convergence theorem for immersions with \(L^2\)-bounded second fundamental form
• Compactness of immersions with local Lipschitz representation
• Asymptotic behavior for singularities of the mean curvature flow
• An Arzela-Ascoli theorem for immersed submanifolds
• A compactness theorem for surfaces with \(L_ p\)-bounded second fundamental form
• The Willmore flow with small initial energy.
• Existence of integral \(m\)-varifolds minimizing \(\int |A|^p\) and \(\int |H|^p\), \(p>m\), in Riemannian manifolds
• Immersions with bounded curvature
• Differential Topology
• Gradient Flow for the Willmore Functional in Riemannian Manifolds of bounded Geometry
• Variational Methods
• Finiteness Theorems for Riemannian Manifolds
• On hypersurfaces in \(\mathbb{R}^{n+1}\) with integral bounds on curvature.

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