In this thesis, I studied Lorentz invariant spacelike surfaces with constant mean curvature H = c in the anti-de Sitter 3-space H31(−c2) of constant curvature −c2. In particular, I construct Lorentz invariant spacelike surfaces of constant mean curvature c and maximal Lorentz invariant spacelike surfaces in H31(−c2). I also studied the limit behavior of those constant mean curvature c surfaces in H31(−c2). It turns out that they approach a maximal catenoid in Minkowski 3-space E31 as c → 0. The limit maximal catenoid is Lorentz invariant in E31.
","abstract_html":"<p>In this thesis, I studied Lorentz invariant spacelike surfaces with constant mean curvature <em>H</em><em> </em>= <em>c</em><em> </em>in the anti-de Sitter 3-space H<sup>3</sup><sub>1</sub>(<em>−c</em><sup>2</sup>) of constant curvature <em>−c</em><sup>2</sup>. In particular, I construct Lorentz invariant spacelike surfaces of constant mean curvature <em>c</em><em> </em>and maximal Lorentz invariant spacelike surfaces in H<sup>3</sup><sub>1</sub>(<em>−c</em><sup>2</sup>). I also studied the limit behavior of those constant mean curvature <em>c</em><em> </em>surfaces in H<sup>3</sup><sub>1</sub>(<em>−c</em><sup>2</sup>). It turns out that they approach a maximal catenoid in Minkowski 3-space E<sup>3</sup><sub>1</sub> as <em>c</em><em> </em><em>→</em><em> </em>0. The limit maximal catenoid is Lorentz invariant in E<sup>3</sup><sub>1</sub>.</p>","abstract_has_math":false,"creators":["Lambert, Jamie Patrick"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Sungwook Lee","James Lambers","William Hornor"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-08-01T07:00:00Z","date_published":"2015-08-01T07:00:00Z","updated_at":"2026-07-24T05:44:34Z","subjects":["CMC","anti-de Sitter","Lorentz invariant spacelike surfaces","maximal surfaces","Geometry and Topology","Mathematics","Physics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/119","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Sungwook Lee","James Lambers","William Hornor"]},{"key":"dc:creator","label":"Author","values":["Lambert, Jamie Patrick"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-06-25T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["CMC","anti-de Sitter","Lorentz invariant spacelike surfaces","maximal surfaces","Geometry and Topology","Mathematics","Physics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/119"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, I studied Lorentz invariant spacelike surfaces with constant mean curvature H = c in the anti-de Sitter 3-space H31(−c2) of constant curvature −c2. In particular, I construct Lorentz invariant spacelike surfaces of constant mean curvature c and maximal Lorentz invariant spacelike surfaces in H31(−c2). I also studied the limit behavior of those constant mean curvature c surfaces in H31(−c2). It turns out that they approach a maximal catenoid in Minkowski 3-space E31 as c → 0. The limit maximal catenoid is Lorentz invariant in E31.
"]},{"key":"dc:title","label":"Title","values":["Lorentz Invariant Spacelike Surfaces of Constant Mean Curvature in Anti-de Sitter 3-Space"]}]}],"canonical_facts":{"dc:contributor":["Sungwook Lee","James Lambers","William Hornor"],"dc:creator":["Lambert, Jamie Patrick"],"dc:date.available":["2015-06-25T07:00:00Z"],"dc:description.abstract":["In this thesis, I studied Lorentz invariant spacelike surfaces with constant mean curvature H = c in the anti-de Sitter 3-space H31(−c2) of constant curvature −c2. In particular, I construct Lorentz invariant spacelike surfaces of constant mean curvature c and maximal Lorentz invariant spacelike surfaces in H31(−c2). I also studied the limit behavior of those constant mean curvature c surfaces in H31(−c2). It turns out that they approach a maximal catenoid in Minkowski 3-space E31 as c → 0. The limit maximal catenoid is Lorentz invariant in E31.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/119"],"dc:subject":["CMC","anti-de Sitter","Lorentz invariant spacelike surfaces","maximal surfaces","Geometry and Topology","Mathematics","Physics"],"dc:title":["Lorentz Invariant Spacelike Surfaces of Constant Mean Curvature in Anti-de Sitter 3-Space"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:44:34Z"}