{"id":8747,"date":"2023-09-15T00:53:28","date_gmt":"2023-09-15T00:53:28","guid":{"rendered":"https:\/\/scm.iec.cat\/?post_type=conference&#038;p=8747"},"modified":"2023-09-29T10:19:17","modified_gmt":"2023-09-29T10:19:17","slug":"joan-hernandez","status":"publish","type":"conference","link":"https:\/\/scm.iec.cat\/eng\/conference\/joan-hernandez\/","title":{"rendered":"2023-TFM-Joan Hernandez"},"content":{"rendered":"<h5>Abstract<\/h5>\n<p>En aquesta xerrada comen\u00e7arem introduint la noci\u00f3 de capacitat anal\u00edtica aix\u00ed com algunes de les seves propietats essencials. Utilitzant aquest concepte identifiquem la fam\u00edlia de subconjunts evitables del pla complex, que s\u00f3n aquells tals que, per a qualsevol funci\u00f3 holomorfa fitada definida en el seu complementari, permeten estendre-la anal\u00edticament a tot el pla. A partir d&#8217;aqu\u00ed, discutim una possible caracteritzaci\u00f3 geom\u00e8trica per a subconjunts evitables, una q\u00fcesti\u00f3 popularment coneguda com el problema de Painlev\u00e9. L&#8217;estudi anterior es realitza en termes de la dimensi\u00f3 de Hausdorff d&#8217;aquests subconjunts, obtenint una classificaci\u00f3 completa per a valors diferents d&#8217;1. El cas restant, l&#8217;associat a la dimensi\u00f3 cr\u00edtica de la capacitat anal\u00edtica, s&#8217;ha de tractar a part. \u00c9s en aquest punt quan invoquem la teoria d&#8217;integrals singulars per tal d&#8217;estudiar una subfam\u00edlia d&#8217;aquests subconjunts: els continguts en gr\u00e0fiques de funcions Lipschitz. Acabarem donant unes pinzellades del tractament d&#8217;aquest cas, introduit per Arnaud Denjoy a principis del segle XX.<\/p>\n<p>&nbsp;<\/p>","protected":false},"featured_media":0,"parent":0,"template":"","categoria_sessions_conferences":[141],"class_list":["post-8747","conference","type-conference","status-publish","hentry","categoria_sessions_conferences-1a-jornada-tfm-2023"],"acf":[],"_links":{"self":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/conference\/8747","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/conference"}],"about":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/types\/conference"}],"wp:attachment":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/media?parent=8747"}],"wp:term":[{"taxonomy":"categoria_sessions_conferences","embeddable":true,"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/categoria_sessions_conferences?post=8747"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}