Isometric embeddings via heat kernel
Differential Geometry
2013-12-06 v4 Spectral Theory
Abstract
For any n-dimensional compact Riemannian manifold (M,g), we construct a canonical t-family of isometric embeddings I_{t}: M->R^{q(t)}, with t>0 sufficiently small and q(t)>>t^{-n/2}. This is done by intrinsically perturbing the heat kernel embedding introduced in [BBG]. As t->0, asymptotic geometry of the embedded images is discussed.
Cite
@article{arxiv.1305.5613,
title = {Isometric embeddings via heat kernel},
author = {Xiaowei Wang and Ke Zhu},
journal= {arXiv preprint arXiv:1305.5613},
year = {2013}
}
Comments
39 pages. We remove the Einstein condition in the previous version. The isometric embedding is extended to all compact Riemannian manifolds with smooth metrics. The embedding is improved to C^k regularity for any given k. Proofs are simplified, and less relevant results are removed