Spectral Geometry and Asymptotically Conic Convergence
谱理论
2020-12-11 v1 微分几何
摘要
In this paper we define a new convergence called "asymptotically conic convergence" in which a smooth family of Riemannian metrics on a fixed compact manifold degenerate to a metric with isolated conic singularity. Our results are: convergence of the spectrum of the geometric Laplacians and uniform convergence of the corresponding heat kernels and existence of a full asymptotic expansion with uniform convergence for all time. Techniques include: the resolution of a conic singularity using a new "resolution blowup" and microlocal analysis using pseudodifferential operator calculi on manifolds with corners constructed by various (standard and non-standard) blowups.
引用
@article{arxiv.math/0701383,
title = {Spectral Geometry and Asymptotically Conic Convergence},
author = {J. M. Rowlett},
journal= {arXiv preprint arXiv:math/0701383},
year = {2020}
}