{"id":1796,"date":"2024-03-21T11:34:37","date_gmt":"2024-03-21T15:34:37","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2024\/?p=1796"},"modified":"2024-04-04T14:43:35","modified_gmt":"2024-04-04T18:43:35","slug":"lecture-16-discrete-curvature-ii-variational-viewpoint","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2024\/2024\/03\/21\/lecture-16-discrete-curvature-ii-variational-viewpoint\/","title":{"rendered":"Lecture 16\u2014Discrete Curvature II (Variational Viewpoint)"},"content":{"rendered":"<p>In this lecture we wrap up our discussion of discrete curvature, and see how it all fits together into a single unified picture that connects the integral viewpoint, the variational viewpoint, and the <em>Steiner formula<\/em>. Along the way we&#8217;ll touch upon several of the major players in discrete differential geometry, including a discrete version of Gauss-Bonnet, Schl\u00e4fli&#8217;s polyhedral formula, and the cotan Laplace operator\u2014which will be the focus of our next set of lectures.<\/p>\n<p><a href=\"http:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2019\/03\/DDG_458_SP19_Lecture16_DiscreteCurvatureII.pdf\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2019\/03\/DDG_458_SP19_Lecture16_DiscreteCurvatureII.jpg\" alt=\"\" width=\"419\" height=\"243\" \/><\/a><a href=\"https:\/\/brickisland.net\/DDGSpring2021\/wp-content\/uploads\/2019\/03\/DDG_458_SP20_Lecture17_DiscreteCurvatureII.pdf\">Here<\/a> are the slides from 2021.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this lecture we wrap up our discussion of discrete curvature, and see how it all fits together into a single unified picture that connects the integral viewpoint, the variational viewpoint, and the Steiner formula. Along the way we&#8217;ll touch upon several of the major players in discrete differential geometry, including a discrete version of &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2024\/2024\/03\/21\/lecture-16-discrete-curvature-ii-variational-viewpoint\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Lecture 16\u2014Discrete Curvature II (Variational Viewpoint)&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":"","_links_to":"","_links_to_target":""},"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/1796"}],"collection":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/comments?post=1796"}],"version-history":[{"count":2,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/1796\/revisions"}],"predecessor-version":[{"id":2391,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/1796\/revisions\/2391"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/media?parent=1796"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/categories?post=1796"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/tags?post=1796"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}