Embeddings of Riemannian manifolds with heat kernels and eigenfunctions

Autor:	Portegies, Jacobus W.
Rok vydání:	2013
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs 58J50 58J35 35P99
Druh dokumentu:	Working Paper
Popis:	We show that any closed n-dimensional Riemannian manifold can be embedded by a map constructed from heat kernels at a certain time from a finite number of points. Both this time and this number can be bounded in terms of the dimension, a lower bound on the Ricci curvature, the injectivity radius and the volume. It follows that the manifold can be embedded by a finite number of eigenfunctions of the Laplace operator. Again, this number only depends on the geometric bounds and the dimension. In addition, both maps can be made arbitrarily close to an isometry. In the appendix, we derive quantitative estimates of the harmonic radius, so that the estimates on the number of eigenfunctions or heat kernels needed can be made quantitative as well. Comment: 29 pages. Appendix added on quantitative estimates of the harmonic radius
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1311.7568 Zobrazit plný text záznamu View this record from Arxiv