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arXiv · 2507.02134

Decoupling for degenerate hypersurfaces

Jianhui Li·Tongou Yang
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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 $\mathbb R^4$ and graphs of homogeneous polynomials in $\mathbb R^5$.

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Jianhui Li, Tongou Yang. 2025-07-02. Decoupling for degenerate hypersurfaces. https://arxiv.org/abs/2507.02134

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