A sharp Sobolev principle on the graphic submanifolds of \(\mathbb{R}^{n+m}\)

DOI10.1007/s12220-023-01534-0OpenAlexW4391215451MaRDI QIDQ6154385

Jie Xiao, Fanheng Xu

Publication date: 15 February 2024

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

Full work available at URL: https://doi.org/10.1007/s12220-023-01534-0

zbMATH Keywords

Sobolev-type inequalitygraphic submanifold

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Rigidity results (53C24) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Cites Work

• Elliptic PDE's in probability and geometry: Symmetry and regularity of solutions
• A sharp Sobolev trace inequality for the fractional-order derivatives
• A general Bieberbach inequality
• The isoperimetric inequality for a minimal submanifold in Euclidean space
• The Logarithmic Sobolev Inequality for a Submanifold in Euclidean Space
• Convex Bodies The Brunn-MinkowskiTheory
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ
• Proof of the Michael-Simon-Sobolev inequality using optimal transport
• Minimal hypersurfaces and geometric inequalities

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