{"id":482,"date":"2022-03-22T14:54:39","date_gmt":"2022-03-22T21:54:39","guid":{"rendered":"\/wp\/hades\/?p=482"},"modified":"2022-03-22T14:54:39","modified_gmt":"2022-03-22T21:54:39","slug":"construction-of-initial-data-for-the-einstein-equation","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2022\/03\/22\/construction-of-initial-data-for-the-einstein-equation\/","title":{"rendered":"Construction of Initial Data for the Einstein Equation"},"content":{"rendered":"\n\t\t\t\t\n<p>The HADES seminar on Tuesday,\u00a0<strong>March 29<\/strong>\u00a0will be at\u00a0<strong>3:30 pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<\/p>\n\n\n\n<p><strong>Speaker<\/strong>: Yuchen Mao<\/p>\n\n\n\n<p><strong>Abstract<\/strong>: Unlike many other equations, initial data for the Einstein equation have to solve the constraint equations, which makes it an interesting problem to construct asymptotically flat localized initial data. Carlotto and Scheon\u00a0proved the existence of gluing construction of such initial data supported in a cone through a functional analytic approach. We give a simpler proof by explicitly constructing a solution with conic support that achieves the optimal decay conjectured by Carlotto, and lower regularity. Another conjecture made by Carlotto is whether we can construct initial\u00a0data localized in a smaller region without violating the positive mass theorem. As an application of our solution operator, we prove this is possible for the case of a degenerate sector. This is a joint work with Zhongkai Tao.<br><\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0March 29\u00a0will be at\u00a03:30 pm\u00a0in\u00a0Room 740. Speaker: Yuchen Mao Abstract: Unlike many other equations, initial data for the Einstein equation have to solve the constraint equations, which makes it an interesting problem to construct asymptotically flat localized initial data. Carlotto and Scheon\u00a0proved the existence of gluing construction of such initial data [&hellip;]<\/p>\n","protected":false},"author":91,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-482","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/482","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/91"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=482"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/482\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=482"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=482"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=482"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}