{"id":1154,"date":"2024-10-09T10:08:09","date_gmt":"2024-10-09T17:08:09","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1154"},"modified":"2024-10-09T10:08:09","modified_gmt":"2024-10-09T17:08:09","slug":"a-support-preserving-homotopy-for-the-de-rham-complex-with-boundary-decay-estimates","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2024\/10\/09\/a-support-preserving-homotopy-for-the-de-rham-complex-with-boundary-decay-estimates\/","title":{"rendered":"A support preserving homotopy for the de Rham complex with boundary decay estimates"},"content":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0<strong>October 15th<\/strong>, will be at\u00a0<strong>2<\/strong><strong>:00pm<\/strong>\u00a0in\u00a0<strong>Room 740.<\/strong><\/p>\n<p><strong>Speaker:<\/strong> <a href=\"https:\/\/mathematics.stanford.edu\/people\/andrea-nuetzi\">Andrea Nuetzi<\/a><\/p>\n<p><strong>Abstract:<\/strong> We construct a chain homotopy for the de Rham complex of relative differential forms on compact manifolds with boundary. This chain homotopy has desirable support propagation properties, and satisfies estimates relative to weighted Sobolev norms, where the weights measure decay near the boundary. The estimates are optimal given the homogeneity properties of the de Rham differential under boundary dilation. When applied to the radial compactification of Euclidean space, this construction yields, in particular, a right inverse of the divergence operator that preserves support on large balls around the origin, and satisfies estimates that measure decay near infinity. I will explain how this right inverse can then be used to also obtain a right inverse of the divergence operator on symmetric traceless matrices in three dimensions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0October 15th, will be at\u00a02:00pm\u00a0in\u00a0Room 740. Speaker: Andrea Nuetzi Abstract: We construct a chain homotopy for the de Rham complex of relative differential forms on compact manifolds with boundary. This chain homotopy has desirable support propagation properties, and satisfies estimates relative to weighted Sobolev norms, where the weights measure decay near [&hellip;]<\/p>\n","protected":false},"author":92,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[],"class_list":["post-1154","post","type-post","status-publish","format-standard","hentry","category-fall-2024"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1154","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\/92"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1154"}],"version-history":[{"count":3,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1154\/revisions"}],"predecessor-version":[{"id":1157,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1154\/revisions\/1157"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1154"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1154"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}