Density and spectrum of minimal submanifolds in space forms

DOI10.1007/s00208-016-1360-yzbMath1377.58027arXiv1407.5280OpenAlexW3099566776MaRDI QIDQ343162

Franciane de Brito Vieira, Barnabé Pessoa Lima, Luciano Mari, José Fábio Bezerra Montenegro

Publication date: 25 November 2016

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.5280

zbMATH Keywords

second fundamental formEuclidean spacecurvaturehyperbolic spaceminimal submanifolddensity functionspace formPlateau's problemLaplace-Beltrami spectrum

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Calabi-Yau theory (complex-analytic aspects) (32Q25) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) PDEs on manifolds (35R01)

Related Items (5)

The spectrum of the Laplacian and volume growth of proper minimal submanifolds ⋮ Mean curvature, volume and properness of isometric immersions ⋮ Spectrum Estimates and Applications to Geometry ⋮ Asymptotically extrinsic tamed submanifolds ⋮ Ends, fundamental tones, and capacities of minimal submanifolds via extrinsic comparison theory

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