{"id":191,"date":"2019-01-14T13:48:59","date_gmt":"2019-01-14T15:48:59","guid":{"rendered":"http:\/\/www.professores.uff.br\/vitorbalestro\/?page_id=191"},"modified":"2019-01-14T13:48:59","modified_gmt":"2019-01-14T15:48:59","slug":"duality-of-gauges-and-symplectic-forms-in-vector-spaces","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/vitorbalestro\/duality-of-gauges-and-symplectic-forms-in-vector-spaces\/","title":{"rendered":"Duality of gauges and symplectic forms in vector spaces"},"content":{"rendered":"<p>V. Balestro, H. Martini and R. Teixeira, <strong>Duality of gauges and symplectic forms in vector spaces<\/strong>, Preprint, 2019. (<a href=\"https:\/\/arxiv.org\/abs\/1901.03421\">arXiv link<\/a>)<\/p>\n<p>Comments: A <em>gauge<\/em> in a vector space is given by a convex body containing the origin as an interior point. We use the identification between an even-dimensional vector field and its dual space given by a fixed symplectic form to introduce a (skew-)dual gauge.\u00a0 This is the gauge whose unit ball is the image of the polar body under the described identification. As a consequence of this construction, we prove that closed characteristics in the boundary of a smooth convex body are optimal cases of an isoperimetric inequality which involves symplectic area and length measured in the dual gauge.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>V. Balestro, H. Martini and R. Teixeira, Duality of gauges and symplectic forms in vector spaces, Preprint, 2019. (arXiv link) Comments: A gauge in a vector space is given by a convex body containing the origin as an interior point. We use the identification between an even-dimensional vector field and its dual space given by [&hellip;]<\/p>\n","protected":false},"author":205,"featured_media":0,"parent":0,"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-191","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/191","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=191"}],"version-history":[{"count":1,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/191\/revisions"}],"predecessor-version":[{"id":192,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/191\/revisions\/192"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/media?parent=191"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/categories?post=191"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/tags?post=191"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}