{"id":1690,"date":"2023-06-08T16:44:10","date_gmt":"2023-06-08T08:44:10","guid":{"rendered":"https:\/\/blog.vanabel.cn\/?p=1690"},"modified":"2023-06-08T16:44:37","modified_gmt":"2023-06-08T08:44:37","slug":"a-short-proof-of-allards-and-brakkes-regularity-theorems","status":"publish","type":"post","link":"https:\/\/blog.vanabel.cn\/?p=1690","title":{"rendered":"A short proof of Allard&#8217;s and Brakke&#8217;s regularity theorems"},"content":{"rendered":"<p>Title: A short proof of Allard&#8217;s and Brakke&#8217;s regularity theorems<br \/>\nAuthors: Guido De Philippis, Carlo Gasparetto, Felix Schulze<br \/>\nCategories: math.AP math.DG<br \/>\n\\\\<br \/>\n We give new short proofs of Allard&#8217;s regularity theorem for varifolds with<br \/>\nbounded first variation and Brakke&#8217;s regularity theorem for integral Brakke<br \/>\nflows with bounded forcing. They are based on a decay of flatness, following<br \/>\nfrom weighted versions of the respective monotonicity formulas, together with a<br \/>\ncharacterization of non-homogeneous blow-ups using the viscosity approach<br \/>\nintroduced by Savin.<br \/>\n\\\\ ( https:\/\/arxiv.org\/abs\/2306.02490 ,  21kb)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Title: A short proof of Allard&#8217;s and Brakke&#038;#8217&hellip; <a class=\"more-link\" href=\"https:\/\/blog.vanabel.cn\/?p=1690\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">A short proof of Allard&#8217;s and Brakke&#8217;s regularity theorems<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[248],"tags":[311,222,312,315,230,313,314],"class_list":["post-1690","post","type-post","status-publish","format-standard","hentry","category-arxiv","tag-allards-regularity-theorem","tag-blowup","tag-brakkes-regularity-theorem","tag-monotonicity-formulas","tag-mustread","tag-varifolds","tag-viscosity-approach","entry"],"_links":{"self":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1690","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1690"}],"version-history":[{"count":1,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1690\/revisions"}],"predecessor-version":[{"id":1691,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1690\/revisions\/1691"}],"wp:attachment":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1690"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1690"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1690"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}