Decoupling for degenerate hypersurfaces

2025/07/02 by Li, Jianhui, Yang, Tongou
#42B99 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.02134

Abstract

We utilise the two principles of decoupling introduced in arXiv:2407.16108 to prove the following conditional result: assuming uniform decoupling for graphs of polynomials in all dimensions with identically zero Gaussian curvature, we can prove decoupling for all smooth hypersurfaces in all dimensions. Moreover, we are able to prove (unconditional) decoupling for all smooth hypersurfaces in \mathbb R⁴ and graphs of homogeneous polynomials in \mathbb R⁵.

Citations

• Decoupling for surfaces with radial symmetry
• Two principles of decoupling
• Decoupling for Ruled Hypersurfaces Generated by a Curve
• Decoupling via Scale-based Approximations of Limited Efficacy
• Decouplings for Real Analytic Surfaces of Revolution
• Decouplings for Surfaces of Zero Curvature
• The proof of the l² Decoupling Conjecture
• Quasi-translations and singular Hessians
• Decouplings for curves and hypersurfaces with nonzero Gaussian curvature

Related

• l^p decouplings for hypersurfaces with nonzero Gaussian curvature
• l² Decoupling for certain degenerate surfaces in ℝ⁴
• Decoupling for smooth surfaces in ℝ³
• Decouplings for curves and hypersurfaces with nonzero Gaussian curvature
• Decoupling for surfaces with radial symmetry