Sharp Poincaré–Wirtinger remainders and spectral stability on stratified Lie groups

Gulaiym Oralsyn

2026

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Data confidence 70 medium

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Abstract

In this paper, we use the spectral resolution of the form-defined Neumann sub-Laplacian to represent the deficit in the sharp Poincaré–Wirtinger inequality on stratified Lie groups. It identifies the complete equality space and yields sharp stability estimates in both the L² distance and the energy distance. The optimal constants are determined by the gap between the first two distinct positive Neumann eigenvalues. We also derive an exact modal evolution law and the optimal uniform decay of the deficit along the Neumann subelliptic heat flow.