English

Unique continuation estimates on manifolds with Ricci curvature bounded below

Analysis of PDEs 2024-02-09 v2 Mathematical Physics Differential Geometry Functional Analysis math.MP Spectral Theory

Abstract

We prove quantitative unique continuation estimates for relatively dense sets and spectral subspaces associated to small energies of Schr\"odinger operators on Riemannian manifolds with Ricci curvature bounded below. The upper bound for the energy range and the constant appearing in the estimate are given in terms of the lower bound of the Ricci curvature and the parameters of the relatively dense set.

Keywords

Cite

@article{arxiv.2305.06916,
  title  = {Unique continuation estimates on manifolds with Ricci curvature bounded below},
  author = {Christian Rose and Martin Tautenhahn},
  journal= {arXiv preprint arXiv:2305.06916},
  year   = {2024}
}

Comments

25 pages, comments welcome!