{"id":309,"date":"2021-09-21T11:38:40","date_gmt":"2021-09-21T11:38:40","guid":{"rendered":"https:\/\/geometry.ulb.ac.be\/bowl\/?page_id=309"},"modified":"2021-11-22T09:20:39","modified_gmt":"2021-11-22T09:20:39","slug":"panagiota-daskalopoulos-columbia","status":"publish","type":"page","link":"https:\/\/geometry.ulb.ac.be\/bowl\/panagiota-daskalopoulos-columbia\/","title":{"rendered":"Panagiota Daskalopoulos (Columbia)"},"content":{"rendered":"\n<p>Panagiota Daskalopoulos will talk on 30th November at 2pm UK time, 3pm Belgian time. Panagiota&#8217;s title is <em>&#8220;Type II smoothing in Mean curvature flow&#8221;<\/em> and her abstract is below. <\/p>\n\n\n\n<!--more-->\n\n\n\n<h4 class=\"wp-block-heading\">Type II smoothing in Mean curvature flow\u00a0<\/h4>\n\n\n\n<p><em>In 1994 Vel\u00e1zquez\u00a0constructed a smooth O(4)xO(4) invariant\u00a0Mean Curvature Flow that forms a type-II singularity at the origin in space-time.\u00a0 Recently,\u00a0Stolarski showed that the mean curvature on this solution is uniformly bounded.\u00a0\u00a0Earlier, Vel\u00e1zquez also provided formal asymptotic expansions for a possible smooth continuation of the solution after the singularity.\u00a0<\/em><\/p>\n\n\n\n<p><em>Jointly with S. Angenent and N. Sesum we\u00a0establish the\u00a0short time existence of Vel\u00e1zquez&#8217; formal continuation, and we verify that the mean curvature is also uniformly bounded on the continuation. Combined with the earlier results of Vel\u00e1zquez&#8211;Stolarski we therefore show that there exists a solution {M_t^7\\subset R^8 | -t_0 &lt;t&lt;t_0} that has an isolated singularity at the origin 0 in R^8, and at t=0; moreover, the mean curvature is uniformly bounded on this solution, even though the second fundamental form is unbounded near the singularity.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Panagiota Daskalopoulos will talk on 30th November at 2pm UK time, 3pm Belgian time. Panagiota&#8217;s title is &#8220;Type II smoothing in Mean curvature flow&#8221; and her abstract is below.<\/p>\n","protected":false},"author":1,"featured_media":59,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"class_list":{"0":"post-309","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"entry"},"featured_image_src":"https:\/\/geometry.ulb.ac.be\/bowl\/wp-content\/uploads\/sites\/8\/2020\/08\/Horizontal-slide-vase-by-rgieseking-600x400.jpg","featured_image_src_square":"https:\/\/geometry.ulb.ac.be\/bowl\/wp-content\/uploads\/sites\/8\/2020\/08\/Horizontal-slide-vase-by-rgieseking-600x600.jpg","_links":{"self":[{"href":"https:\/\/geometry.ulb.ac.be\/bowl\/wp-json\/wp\/v2\/pages\/309","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/geometry.ulb.ac.be\/bowl\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/geometry.ulb.ac.be\/bowl\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/geometry.ulb.ac.be\/bowl\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/geometry.ulb.ac.be\/bowl\/wp-json\/wp\/v2\/comments?post=309"}],"version-history":[{"count":2,"href":"https:\/\/geometry.ulb.ac.be\/bowl\/wp-json\/wp\/v2\/pages\/309\/revisions"}],"predecessor-version":[{"id":327,"href":"https:\/\/geometry.ulb.ac.be\/bowl\/wp-json\/wp\/v2\/pages\/309\/revisions\/327"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/geometry.ulb.ac.be\/bowl\/wp-json\/wp\/v2\/media\/59"}],"wp:attachment":[{"href":"https:\/\/geometry.ulb.ac.be\/bowl\/wp-json\/wp\/v2\/media?parent=309"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}