Uniformity of Maximal Hypoellipticity on Graded Lie Groups: From Pointwise to Global

2025/12/14 by Shi-Qi Liu, Edward McDonald, Liu, Shiqi +5
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Geometry and complex manifolds #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2512.12646

openalex publication_date 2025/12/14 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

Abstract

On graded Lie groups, we develop a mechanism that transfers the uniformity of maximal hypoellipcity from the frozen coefficients principal part of a differential operator to the full operator. Our approach brings the century-old "freeze-unfreeze" strategy into the hypoelliptic setting, and offers a transparent and flexible framework for lifting symbol-level hypoelliptic properties to global elliptic estimates, without relying on pseudodifferential calculus. In addition, we prove that symmetric operators of hypoelliptic type on a graded Lie group are self-adjoint.

Citations

• Spectral estimates and asymptotics for stratified Lie groups

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