{"id":1528,"date":"2023-06-01T15:00:28","date_gmt":"2023-06-01T07:00:28","guid":{"rendered":"https:\/\/blog.vanabel.cn\/blog\/2023\/06\/01\/title-a-note-on-serrins-type-problem-on\/"},"modified":"2023-06-01T15:03:34","modified_gmt":"2023-06-01T07:03:34","slug":"title-a-note-on-serrins-type-problem-on","status":"publish","type":"post","link":"https:\/\/blog.vanabel.cn\/?p=1528","title":{"rendered":"Title A note on Serrin&#8217;s type problem on&#8230;"},"content":{"rendered":"<p>Title: A note on Serrin&#8217;s type problem on Riemannian manifolds<br \/>\nAuthors: Allan Freitas, Alberto Roncoroni and M\\&#8217;arcio Santos<br \/>\nCategories: math.DG math.AP<br \/>\nComments: Comments are welcome!<br \/>\n\\\\<br \/>\n In this paper, we deal with Serrin-type problems in Riemannian manifolds.<br \/>\nFirst, we obtain a Heintze-Karcher inequality and a Soap Bubble result, with<br \/>\nits respective rigidity, when the ambient space has a Ricci tensor bounded<br \/>\nbelow. After, we approach a Serrin problem in bounded domains of manifolds<br \/>\nendowed with a closed conformal vector field. Our primary tool, in this case,<br \/>\nis a new Pohozaev identity, which depends on the scalar curvature of the<br \/>\nmanifold. Applications involve Einstein and constant scalar curvature spaces.<br \/>\n\\\\ ( https:\/\/arxiv.org\/abs\/2305.19772 ,  15kb)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Title: A note on Serrin&#8217;s type problem on Riemann&hellip; <a class=\"more-link\" href=\"https:\/\/blog.vanabel.cn\/?p=1528\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">Title A note on Serrin&#8217;s type problem on&#8230;<\/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":[288,287,289,286],"class_list":["post-1528","post","type-post","status-publish","format-status","hentry","category-arxiv","tag-bubble","tag-heintze-karcher-inequality","tag-pohozaev-identity","tag-serrins-type-problem","post_format-post-format-status","entry"],"_links":{"self":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1528","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=1528"}],"version-history":[{"count":1,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1528\/revisions"}],"predecessor-version":[{"id":1531,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1528\/revisions\/1531"}],"wp:attachment":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1528"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1528"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1528"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}