Decoupling for surfaces with radial symmetry

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This is a Quantitative Study study.

Jianhui Li; Tongou Yang

doi:10.48550/arxiv.2504.17100

April 23, 2025Open Access

Decoupling for surfaces with radial symmetry

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Key Points

Decoupling is proven for two types of surfaces with radial symmetry, significantly advancing geometric analysis.
The first type involves surfaces of revolution in R^n, providing a broader framework for understanding complex geometries.
The second type focuses on graphs of trivariate homogeneous functions, revealing important connections within mathematical structures.
Utilizing previously established decoupling principles, this work highlights the interplay between symmetry and function behavior.

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Implication

This analysis proves decoupling for surfaces of revolution and graphs of smooth functions, indicating a broad application in geometric analysis.

Abstract

We utilise the two principles of decoupling introduced in [arXiv:2407.16108] to prove decoupling for two types of surfaces exhibiting radial symmetry. The first type are surfaces of revolution in Rⁿ generated by smooth surfaces in R³. The second type of surfaces are graphs of trivariate homogeneous smooth functions of a nonzero degree.

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Cite This Study

Li et al. (2025) studied this question.

synapsesocial.com/papers/68f43f92854d1061a58aca96 https://doi.org/10.48550/arxiv.2504.17100

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Decoupling for surfaces with radial symmetry

Key Points

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Implication

Abstract

Discussion

Cite This Study

Decoupling for surfaces with radial symmetry

Key Points

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Implication

Abstract

Discussion

Cite This Study

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