Embedding Riemannian manifolds by the heat kernel of the connection Laplacian

Hau Tieng Wu

doi:10.1016/j.aim.2016.05.023

Embedding Riemannian manifolds by the heat kernel of the connection Laplacian

Hau Tieng Wu

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	1055-1079
Number of pages	25
Journal	Advances in Mathematics
Volume	304
DOIs	https://doi.org/10.1016/j.aim.2016.05.023
State	Published - Jan 2 2017

Keywords

Graph connection Laplacian
Precompactness
Spectral geometry
Spectral graph theory
Vector diffusion map

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1016/j.aim.2016.05.023

Cite this

@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 = "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.",

}

TY - JOUR

T1 - Embedding Riemannian manifolds by the heat kernel of the connection Laplacian

AU - Wu, Hau Tieng

PY - 2017/1/2

Y1 - 2017/1/2

N2 - 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.

AB - 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.

KW - Graph connection Laplacian

KW - Precompactness

KW - Spectral geometry

KW - Spectral graph theory

KW - Vector diffusion map

UR - http://www.scopus.com/inward/record.url?scp=84988462410&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988462410&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2016.05.023

DO - 10.1016/j.aim.2016.05.023

M3 - Article

AN - SCOPUS:84988462410

SN - 0001-8708

VL - 304

SP - 1055

EP - 1079

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Embedding Riemannian manifolds by the heat kernel of the connection Laplacian

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this