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arXiv · 2611.01013

Ground state uniqueness and quantitative stability for the mass-critical Hartree equation

Guangze Gu·Zhipeng Yang
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Abstract

We prove that the ground state of the mass-critical Hartree equation is unique up to phase rotations and translations and nondegenerate in every dimension $d\ge3$. This makes the recent conditional $L^2$ classification of minimal-mass blow-up and non-scattering solutions unconditional; we also give a direct $H^1$ proof of the finite-time blow-up classification. We further establish a global quadratic stability estimate for the sharp Hartree interpolation inequality. For the optimal stability constant, we rule out vanishing of minimizing sequences and describe their possible loss of compactness.

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Guangze Gu, Zhipeng Yang. 2026-10-31. Ground state uniqueness and quantitative stability for the mass-critical Hartree equation. https://arxiv.org/abs/2611.01013

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