An Isomorphism Theorem for Some Linear Elliptic Differential Operators on Quasi-Asymptotically Conical Manifolds

Mohamed Nouidha

An Isomorphism Theorem for Some Linear Elliptic Differential Operators on Quasi-Asymptotically Conical Manifolds

Differential Geometry 2025-06-18 v2 Analysis of PDEs

Authors: Mohamed Nouidha

Abstract

We study a linear elliptic differential operator of the form $\mathcal{P}=\Delta + V - \lambda$ on a quasi-asymptotically conical manifold $(M, g)$ , where $g$ is a polyhomogeneous metric and $V$ is a $b$ -vector field that is unbounded with respect to the metric $g$ .

Keywords

quasi-asymptotically conical manifold linear elliptic differential operator polyhomogeneous metric b-vector field isomorphism theorem differential geometry

Cite

@article{arxiv.2506.13069,
  title  = {An Isomorphism Theorem for Some Linear Elliptic Differential Operators on Quasi-Asymptotically Conical Manifolds},
  author = {Mohamed Nouidha},
  journal= {arXiv preprint arXiv:2506.13069},
  year   = {2025}
}

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