Mass from an Extrinsic Point of View

We express the -th Gauss-Bonnet-Chern mass of an immersed submanifold of Euclidean space as a linear combination of two terms: the total (2)-th mean curvature and the integral, over the entire manifold, of the inner product between the (2 + 1)-th mean curvature vector and the position vector of the...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2025
Hauptverfasser: de Sousa, Alexandre, Girão, Frederico
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2025
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/212873
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Mass from an Extrinsic Point of View. Alexandre de Sousa and Frederico Girão. SIGMA 21 (2025), 018, 11 pages

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
_version_ 1862579788053479424
author de Sousa, Alexandre
Girão, Frederico
author_facet de Sousa, Alexandre
Girão, Frederico
citation_txt Mass from an Extrinsic Point of View. Alexandre de Sousa and Frederico Girão. SIGMA 21 (2025), 018, 11 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We express the -th Gauss-Bonnet-Chern mass of an immersed submanifold of Euclidean space as a linear combination of two terms: the total (2)-th mean curvature and the integral, over the entire manifold, of the inner product between the (2 + 1)-th mean curvature vector and the position vector of the immersion. As a consequence, we obtain, for each , a geometric inequality that holds whenever the positive mass theorem (for the -th Gauss-Bonnet-Chern mass) holds.
first_indexed 2026-03-21T11:56:48Z
format Article
fulltext
id nasplib_isofts_kiev_ua-123456789-212873
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-21T11:56:48Z
publishDate 2025
publisher Інститут математики НАН України
record_format dspace
spelling de Sousa, Alexandre
Girão, Frederico
2026-02-13T13:49:03Z
2025
Mass from an Extrinsic Point of View. Alexandre de Sousa and Frederico Girão. SIGMA 21 (2025), 018, 11 pages
1815-0659
2020 Mathematics Subject Classification: 83C99; 53C40; 51M16
arXiv:2403.06782
https://nasplib.isofts.kiev.ua/handle/123456789/212873
https://doi.org/10.3842/SIGMA.2025.018
We express the -th Gauss-Bonnet-Chern mass of an immersed submanifold of Euclidean space as a linear combination of two terms: the total (2)-th mean curvature and the integral, over the entire manifold, of the inner product between the (2 + 1)-th mean curvature vector and the position vector of the immersion. As a consequence, we obtain, for each , a geometric inequality that holds whenever the positive mass theorem (for the -th Gauss-Bonnet-Chern mass) holds.
This study was partially financed by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior- Brasil (CAPES) - Finance Code 001. This work was partially done while Alexandre de Sousa was a CAPES Fellow at the Mathematics Institute of Federal University of Alagoas (IM/UFAL), whose members he would like to thank for the hospitality. Frederico Girão was partially supported by CNPq, grant number 307239/2020-9.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Mass from an Extrinsic Point of View
Article
published earlier
spellingShingle Mass from an Extrinsic Point of View
de Sousa, Alexandre
Girão, Frederico
title Mass from an Extrinsic Point of View
title_full Mass from an Extrinsic Point of View
title_fullStr Mass from an Extrinsic Point of View
title_full_unstemmed Mass from an Extrinsic Point of View
title_short Mass from an Extrinsic Point of View
title_sort mass from an extrinsic point of view
url https://nasplib.isofts.kiev.ua/handle/123456789/212873
work_keys_str_mv AT desousaalexandre massfromanextrinsicpointofview
AT giraofrederico massfromanextrinsicpointofview