@article{51469e9af110491980be0b6f9d22e859,
title = "Embedding Riemannian manifolds by the heat kernel of the connection Laplacian",
abstract = "Given a class of closed Riemannian manifolds with prescribed geometric conditions, we introduce an embedding of the manifolds into ℓ2 based on the heat kernel of the Connection Laplacian associated with the Levi-Civita connection on the tangent bundle. As a result, we can construct a distance in this class which leads to a pre-compactness theorem on the class under consideration.",
keywords = "Graph connection Laplacian, Precompactness, Spectral geometry, Spectral graph theory, Vector diffusion map",
author = "Wu, {Hau Tieng}",
note = "Funding Information: The author acknowledges the support partially by FHWA grant DTFH61-08-C-00028 , partially by Award Number FA9550-09-1-0551 from AFOSR and partially by Connaught New Researcher grant 498992 . He acknowledges Professor Charlie Fefferman and Professor Amit Singer for their time and inspiring and helpful discussions; in particular Professor Amit Singer, who introduced him the massive data analysis field. He also acknowledges the valuable discussion with Professor G{\'e}rard Besson, Professor Richard Bamler and Dr. Chen-Yun Lin. The author also thanks the anonymous reviewer's constructive and helpful comments. Publisher Copyright: {\textcopyright} 2016",
year = "2017",
month = jan,
day = "2",
doi = "10.1016/j.aim.2016.05.023",
language = "English (US)",
volume = "304",
pages = "1055--1079",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
}