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PreprintCC BY 4.0arXiv

Determining Schrodinger Potentials on Riemannian Manifolds

  • Lu Chen
  • Yan Jiang
  • Hongyu Liu
  • Longyue Tao
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Abstract

We prove that the Dirichlet-to-Neumann map uniquely determines a smooth real Schrödinger potential on any prescribed compact connected smooth Riemannian manifold of dimension at least three with nonempty smooth boundary. The proof combines local continuation of Green kernels with uniform estimates for the associated integral representations on shrinking spheres. These estimates yield local recovery of the potential, and a continuation argument extends this recovery throughout the manifold.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026determining,
  title = {{Determining Schrodinger Potentials on Riemannian Manifolds}},
  author = {Lu Chen and Yan Jiang and Hongyu Liu and Longyue Tao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.18711},
  eprint = {2609.18711},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18711},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Determining Schrodinger Potentials on Riemannian Manifolds
AU  - Lu Chen
AU  - Yan Jiang
AU  - Hongyu Liu
AU  - Longyue Tao
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.18711
UR  - https://arxiv.org/abs/2609.18711
AB  - We prove that the Dirichlet-to-Neumann map uniquely determines a smooth real Schrödinger potential on any prescribed compact connected smooth Riemannian manifold of dimension at least three with nonempty smooth boundary. The proof combines local continuation of Green kernels with uniform estimates for the associated integral representations on shrinking spheres. These estimates yield local recovery of the potential, and a continuation argument extends this recovery throughout the manifold.
ER  -