{"id":1705,"date":"2023-06-09T15:40:38","date_gmt":"2023-06-09T07:40:38","guid":{"rendered":"https:\/\/blog.vanabel.cn\/?p=1705"},"modified":"2023-06-09T15:40:38","modified_gmt":"2023-06-09T07:40:38","slug":"existence-of-closed-embedded-curves-of-constant-curvature-via-min-max","status":"publish","type":"post","link":"https:\/\/blog.vanabel.cn\/?p=1705","title":{"rendered":"Existence of closed embedded curves of constant curvature via min-max"},"content":{"rendered":"<p>Title: Existence of closed embedded curves of constant curvature via min-max<br \/>\nAuthors: Lorenzo Sarnataro, Douglas Stryker<br \/>\nCategories: math.DG math.DS<br \/>\nComments: 26 pages<br \/>\n\\\\<br \/>\n We find conditions under which Almgren-Pitts min-max for the prescribed<br \/>\ngeodesic curvature functional in a closed oriented Riemannian surface produces<br \/>\na closed embedded curve of constant curvature. In particular, we find a closed<br \/>\nembedded curve of any prescribed constant curvature in any metric on $S^2$ with<br \/>\n$1\/8$-pinched Gaussian curvature.<br \/>\n\\\\ ( https:\/\/arxiv.org\/abs\/2306.04840 ,  29kb)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Title: Existence of closed embedded curves of constant &hellip; <a class=\"more-link\" href=\"https:\/\/blog.vanabel.cn\/?p=1705\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">Existence of closed embedded curves of constant curvature via min-max<\/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":[318,320,321,319],"class_list":["post-1705","post","type-post","status-publish","format-standard","hentry","category-arxiv","tag-almgren-pitts","tag-constant-curvature","tag-interest","tag-min-max","entry"],"_links":{"self":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1705","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=1705"}],"version-history":[{"count":1,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1705\/revisions"}],"predecessor-version":[{"id":1706,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1705\/revisions\/1706"}],"wp:attachment":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1705"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1705"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1705"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}