{"id":76,"date":"2018-11-09T11:47:26","date_gmt":"2018-11-09T13:47:26","guid":{"rendered":"http:\/\/www.professores.uff.br\/vitorbalestro\/?page_id=76"},"modified":"2018-11-09T11:47:26","modified_gmt":"2018-11-09T13:47:26","slug":"on-curvature-of-surfaces-immersed-in-normed-spaces","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/vitorbalestro\/publications\/on-curvature-of-surfaces-immersed-in-normed-spaces\/","title":{"rendered":"On curvature of surfaces immersed in normed spaces"},"content":{"rendered":"<p id=\"h.p_-7sg913j_j5m\" class=\"zfr3Q\">V. Balestro, H. Martini and Ralph Teixeira, <strong>On curvature of surfaces immersed in normed spaces<\/strong>, preprint, 2018. (<a class=\"dhtgD\" href=\"https:\/\/www.google.com\/url?q=https%3A%2F%2Farxiv.org%2Fabs%2F1805.02045&amp;sa=D&amp;sntz=1&amp;usg=AFQjCNFZgnE-l5ql3FjB7RldGm6eXIYbgQ\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv link<\/a>)<\/p>\n<p id=\"h.p_R6LVBizn_pqd\" class=\"zfr3Q\">Comments: In this paper we explore a little deeper the properties of Minkowski Gaussian and mean curvatures of a surface immersed in a three-dimensional space endowed with a norm. Several results analogous to the Euclidean case are obtained. The most interesting, in our opinion, is an extension of Alexandrov&#8217;s theorem, which states that any embedded compact surface without boundary whose Minkowski mean curvature is constant must be a Minkowski sphere (that is, a sphere of the ambient norm). Planar versions of some results are also discussed, as well as some problems.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>V. Balestro, H. Martini and Ralph Teixeira, On curvature of surfaces immersed in normed spaces, preprint, 2018. (arXiv link) Comments: In this paper we explore a little deeper the properties of Minkowski Gaussian and mean curvatures of a surface immersed in a three-dimensional space endowed with a norm. Several results analogous to the Euclidean case [&hellip;]<\/p>\n","protected":false},"author":205,"featured_media":0,"parent":12,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[],"tags":[],"class_list":["post-76","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/76","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/users\/205"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/comments?post=76"}],"version-history":[{"count":1,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/76\/revisions"}],"predecessor-version":[{"id":77,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/76\/revisions\/77"}],"up":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/12"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/media?parent=76"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/categories?post=76"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/tags?post=76"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}