Mass and Riemannian polyhedra

Pengzi Miao; Annachiara Piubello

doi:10.1016/j.aim.2022.108287

Mass and Riemannian polyhedra

Pengzi Miao, Annachiara Piubello

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

Abstract

We show that the concept of the ADM mass in general relativity can be understood via the total mean curvature and the total defect of dihedral angle of the boundary of large Riemannian polyhedra. We also derive the n-dimensional mass as a suitable integral of quantities determining the (n−1)-dimensional mass.

Original language	English (US)
Article number	108287
Journal	Advances in Mathematics
Volume	400
DOIs	https://doi.org/10.1016/j.aim.2022.108287
State	Published - May 14 2022
Externally published	Yes

Keywords

Mass
Mean curvature
Scalar curvature

ASJC Scopus subject areas

Mathematics(all)

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10.1016/j.aim.2022.108287

Cite this

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title = "Mass and Riemannian polyhedra",

abstract = "We show that the concept of the ADM mass in general relativity can be understood via the total mean curvature and the total defect of dihedral angle of the boundary of large Riemannian polyhedra. We also derive the n-dimensional mass as a suitable integral of quantities determining the (n−1)-dimensional mass.",

keywords = "Mass, Mean curvature, Scalar curvature",

author = "Pengzi Miao and Annachiara Piubello",

note = "Funding Information: The first named author's research was partially supported by NSF grant DMS-1906423 . Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2022",

month = may,

day = "14",

doi = "10.1016/j.aim.2022.108287",

language = "English (US)",

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journal = "Advances in Mathematics",

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T1 - Mass and Riemannian polyhedra

AU - Miao, Pengzi

AU - Piubello, Annachiara

PY - 2022/5/14

Y1 - 2022/5/14

N2 - We show that the concept of the ADM mass in general relativity can be understood via the total mean curvature and the total defect of dihedral angle of the boundary of large Riemannian polyhedra. We also derive the n-dimensional mass as a suitable integral of quantities determining the (n−1)-dimensional mass.

AB - We show that the concept of the ADM mass in general relativity can be understood via the total mean curvature and the total defect of dihedral angle of the boundary of large Riemannian polyhedra. We also derive the n-dimensional mass as a suitable integral of quantities determining the (n−1)-dimensional mass.

KW - Mass

KW - Mean curvature

KW - Scalar curvature

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U2 - 10.1016/j.aim.2022.108287

DO - 10.1016/j.aim.2022.108287

M3 - Article

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VL - 400

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

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ER -

Mass and Riemannian polyhedra

Abstract

Keywords

ASJC Scopus subject areas

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