{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T00:07:43Z","timestamp":1774915663364,"version":"3.50.1"},"reference-count":14,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,5,24]],"date-time":"2020-05-24T00:00:00Z","timestamp":1590278400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004497","name":"Onderzoeksraad, KU Leuven","doi-asserted-by":"publisher","award":["3E160361"],"award-info":[{"award-number":["3E160361"]}],"id":[{"id":"10.13039\/501100004497","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003130","name":"Fonds Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["G0F2319N"],"award-info":[{"award-number":["G0F2319N"]}],"id":[{"id":"10.13039\/501100003130","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003130","name":"Fonds Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["EOS project G0H4518N"],"award-info":[{"award-number":["EOS project G0H4518N"]}],"id":[{"id":"10.13039\/501100003130","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A marginally trapped surface in a spacetime is a Riemannian surface whose mean curvature vector is lightlike at every point. In this paper we give an up-to-date overview of the differential geometric study of these surfaces in Minkowski, de Sitter, anti-de Sitter and Robertson-Walker spacetimes. We give the general local descriptions proven by Anciaux and his coworkers as well as the known classifications of marginally trapped surfaces satisfying one of the following additional geometric conditions: having positive relative nullity, having parallel mean curvature vector field, having finite type Gauss map, being invariant under a one-parameter group of ambient isometries, being isotropic, being pseudo-umbilical. Finally, we provide examples of constant Gaussian curvature marginally trapped surfaces and state some open questions.<\/jats:p>","DOI":"10.3390\/axioms9020060","type":"journal-article","created":{"date-parts":[[2020,5,25]],"date-time":"2020-05-25T06:43:40Z","timestamp":1590389020000},"page":"60","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Geometric Study of Marginally Trapped Surfaces in Space Forms and Robertson-Walker Spacetimes\u2014An Overview"],"prefix":"10.3390","volume":"9","author":[{"given":"Kristof","family":"Dekimpe","sequence":"first","affiliation":[{"name":"Department of Mathematics, KU Leuven, Celestijnenlaan 200B, Box 2400, 3001 Leuven, Belgium"}]},{"given":"Joeri","family":"Van der Veken","sequence":"additional","affiliation":[{"name":"Department of Mathematics, KU Leuven, Celestijnenlaan 200B, Box 2400, 3001 Leuven, Belgium"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1103\/PhysRevLett.14.57","article-title":"Gravitational collapse and space-time singularities","volume":"14","author":"Penrose","year":"1965","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1088\/0264-9381\/24\/3\/003","article-title":"Marginally trapped surfaces in Lorentzian space forms with positive relative nullity","volume":"24","author":"Chen","year":"2007","journal-title":"Class. Quantum Gravity"},{"key":"ref_3","first-page":"421","article-title":"Classification of marginally trapped surfaces with parallel mean curvature vector in Lorentzian space forms","volume":"36","author":"Chen","year":"2010","journal-title":"Houston J. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1621","DOI":"10.1007\/s10714-013-1621-y","article-title":"On the marginally trapped surfaces in 4-dimensional space-times with finite type Gauss map","volume":"46","author":"Turgay","year":"2014","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5441","DOI":"10.1088\/0264-9381\/24\/22\/009","article-title":"Boost invariant marginally trapped surfaces in Minkowski 4-space","volume":"24","author":"Haesen","year":"2007","journal-title":"Class. Quantum Gravity"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1819","DOI":"10.1007\/s10714-008-0754-x","article-title":"Marginally trapped surfaces in Minkowski 4-space invariant under a rotation subgroup of the Lorentz group","volume":"41","author":"Haesen","year":"2009","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/j.jmaa.2009.02.019","article-title":"Screw invariant marginally trapped surfaces in Minkowski 4-space","volume":"355","author":"Haesen","year":"2009","journal-title":"J. Math. Anal. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"135005","DOI":"10.1088\/0264-9381\/27\/13\/135005","article-title":"Isotropy and marginally trapped surfaces in a spacetime","volume":"27","author":"Cabrerizo","year":"2010","journal-title":"Class. Quantum Gravity"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"313","DOI":"10.5556\/j.tkjm.40.2009.600","article-title":"Black holes, marginally trapped surfaces and quasi-minimal surfaces","volume":"40","author":"Chen","year":"2009","journal-title":"Tamkang J. Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"023502","DOI":"10.1063\/1.4906936","article-title":"Marginally trapped submanifolds in Lorentzian space forms and in the Lorentzian product of a space form by the real line","volume":"56","author":"Anciaux","year":"2015","journal-title":"J. Math. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.geomphys.2014.11.009","article-title":"Codimension two marginally trapped submanifolds in Robertson-Walker spacetimes","volume":"88","author":"Anciaux","year":"2015","journal-title":"J. Geom. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"073509","DOI":"10.1063\/1.2748616","article-title":"Spatial and Lorentzian surfaces in Robertson-Walker space times","volume":"48","author":"Chen","year":"2007","journal-title":"J. Math. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"31","DOI":"10.21099\/tkbjm\/1496159942","article-title":"Isometric immersions of Lorentz space with parallel second fundamental forms","volume":"8","author":"Magid","year":"1984","journal-title":"Tsukuba J. Math."},{"key":"ref_14","unstructured":"Walleghem, L. (2019). Marginally Trapped Surfaces in Space Forms Contained in Null Hypersurfaces or Having Constant Gaussian Curvature. [Master\u2019s Thesis, KU Leuven]."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/9\/2\/60\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:32:04Z","timestamp":1760175124000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/9\/2\/60"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,24]]},"references-count":14,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["axioms9020060"],"URL":"https:\/\/doi.org\/10.3390\/axioms9020060","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,24]]}}}