A survey on the positive mass theorem for asymptotically flat initial data sets
In honor of Yvonne Choquet-Bruhat’s 100th birthday, we present this survey on the positive mass theorem. Originating from a conjecture in general relativity regarding the ADM mass, the positive mass theorem has significantly influenced geometry and analysis over the past four decades and continued t...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2025-01-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.270/ |
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| author | Huang, Lan-Hsuan |
| author_facet | Huang, Lan-Hsuan |
| author_sort | Huang, Lan-Hsuan |
| collection | DOAJ |
| description | In honor of Yvonne Choquet-Bruhat’s 100th birthday, we present this survey on the positive mass theorem. Originating from a conjecture in general relativity regarding the ADM mass, the positive mass theorem has significantly influenced geometry and analysis over the past four decades and continued to inspire new connections. We review seminal contributions as well as recent advances, and then we focus our discussions on the equality case and the counter-examples arising from pp-wave spacetimes. |
| format | Article |
| id | doaj-art-5c8f1ccd3ab94491876d8ec336e8d9a9 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-5c8f1ccd3ab94491876d8ec336e8d9a92025-02-07T13:49:01ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342025-01-01353G117719410.5802/crmeca.27010.5802/crmeca.270A survey on the positive mass theorem for asymptotically flat initial data setsHuang, Lan-Hsuan0https://orcid.org/0000-0002-8918-3071Department of Mathematics, University of Connecticut, Storrs, CT 06269, USAIn honor of Yvonne Choquet-Bruhat’s 100th birthday, we present this survey on the positive mass theorem. Originating from a conjecture in general relativity regarding the ADM mass, the positive mass theorem has significantly influenced geometry and analysis over the past four decades and continued to inspire new connections. We review seminal contributions as well as recent advances, and then we focus our discussions on the equality case and the counter-examples arising from pp-wave spacetimes.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.270/ADM massADM energy-momentumAsymptotically flat initial data setDominant energy conditionpp-wave |
| spellingShingle | Huang, Lan-Hsuan A survey on the positive mass theorem for asymptotically flat initial data sets Comptes Rendus. Mécanique ADM mass ADM energy-momentum Asymptotically flat initial data set Dominant energy condition pp-wave |
| title | A survey on the positive mass theorem for asymptotically flat initial data sets |
| title_full | A survey on the positive mass theorem for asymptotically flat initial data sets |
| title_fullStr | A survey on the positive mass theorem for asymptotically flat initial data sets |
| title_full_unstemmed | A survey on the positive mass theorem for asymptotically flat initial data sets |
| title_short | A survey on the positive mass theorem for asymptotically flat initial data sets |
| title_sort | survey on the positive mass theorem for asymptotically flat initial data sets |
| topic | ADM mass ADM energy-momentum Asymptotically flat initial data set Dominant energy condition pp-wave |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.270/ |
| work_keys_str_mv | AT huanglanhsuan asurveyonthepositivemasstheoremforasymptoticallyflatinitialdatasets AT huanglanhsuan surveyonthepositivemasstheoremforasymptoticallyflatinitialdatasets |