{"id":1337,"date":"2023-05-09T15:18:03","date_gmt":"2023-05-09T07:18:03","guid":{"rendered":"https:\/\/blog.vanabel.cn\/blog\/2023\/05\/09\/https-arxiv-org-abs-2305-04702\/"},"modified":"2023-05-14T00:38:00","modified_gmt":"2023-05-13T16:38:00","slug":"https-arxiv-org-abs-2305-04702","status":"publish","type":"post","link":"https:\/\/blog.vanabel.cn\/?p=1337","title":{"rendered":"Inverse mean curvature flow and Ricci-pinched three-manifolds"},"content":{"rendered":"<p>Inverse mean curvature flow and Ricci-pinched three-manifolds<\/p>\n<p>Gerhard Huisken, Thomas Koerber<br \/>\nLet (M,g) be a complete, connected, non-compact Riemannian three-manifold with non-negative Ricci curvature satisfying Ric\u2265\u03b5tr(Ric)g for some \u03b5>0. In this note, we give a new proof based on inverse mean curvature flow that (M,g) is either flat or has non-Euclidean volume growth. In conjunction with results of J. Lott and of M.-C. Lee and P. Topping, this gives an alternative proof of a conjecture of R. Hamilton recently proven by A. Deruelle, F. Schulze, and M. Simon using Ricci flow.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Inverse mean curvature flow and Ricci-pinched three-man&hellip; <a class=\"more-link\" href=\"https:\/\/blog.vanabel.cn\/?p=1337\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">Inverse mean curvature flow and Ricci-pinched three-manifolds<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"status","meta":{"footnotes":""},"categories":[248],"tags":[215,214,216],"class_list":["post-1337","post","type-post","status-publish","format-status","hentry","category-arxiv","tag-conjecture-of-r-hamilton","tag-inverse-mean-curvature-flow","tag-ricci-flow","post_format-post-format-status","entry"],"_links":{"self":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1337","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=1337"}],"version-history":[{"count":1,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1337\/revisions"}],"predecessor-version":[{"id":1497,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1337\/revisions\/1497"}],"wp:attachment":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1337"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1337"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1337"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}