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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≥3. This makes the recent conditional L2 classification of minimal-mass blow-up and non-scattering solutions unconditional; we also give a direct H1 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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Cite

BibTeXRIS
BibTeX
@misc{gu2026ground,
  title = {{Ground state uniqueness and quantitative stability for the mass-critical Hartree equation}},
  author = {Guangze Gu and Zhipeng Yang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01013},
  eprint = {2611.01013},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01013},
}
RIS
TY  - UNPB
TI  - Ground state uniqueness and quantitative stability for the mass-critical Hartree equation
AU  - Guangze Gu
AU  - Zhipeng Yang
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01013
UR  - https://arxiv.org/abs/2611.01013
AB  - 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≥3. 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.
ER  -