{"id":17028,"date":"2018-03-09T09:04:54","date_gmt":"2018-03-09T09:04:54","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/problemas-sobre-analisis-geometrico-convexo\/"},"modified":"2018-03-09T09:04:54","modified_gmt":"2018-03-09T09:04:54","slug":"problemas-sobre-analisis-geometrico-convexo","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/problemas-sobre-analisis-geometrico-convexo\/","title":{"rendered":"Problemas sobre an\u00e1lisis geom\u00e9trico convexo"},"content":{"rendered":"<h2>Tesis doctoral de <strong>  Romance Del R\u00edo Miguel <\/strong><\/h2>\n<p>El objetivo fundamental de esta tesis es el estudio de dos conceptos b\u00e1sicos del an\u00e1lisis geom\u00e9trico convexo: la isotrop\u00eda y determinadas posiciones notables de cuerpos convexos, haciendo especial hincapi\u00e9 en las relaciones existentes entre ambos t\u00e9rminos. En esta direcci\u00f3n, los principales resultados obtenidos son los siguientes:  1,- se estudian las posiciones de m\u00e1ximo volumen de cuerpos convexo, probando extensiones no convexas del teorema cl\u00e1sico de john que descubren nuevas e interesantes relaciones entre posiciones de m\u00e1ximo volumen y propiedades de tipo isotr\u00f3pico de ciertas medidas de borel soportadas en pares de contacto de los cuerpos.  2,- se investigan diferentes problemas extremales en el contexto de la teor\u00eda dual de brunn-minkowski, prob\u00e1ndose que la isotrop\u00eda de ciertas medidas es condici\u00f3n necesaria y en muchos casos suficiente para caracterizar la soluci\u00f3n a los problemas extremales en teor\u00eda dual y medidas con propiedades de tipo sitotr\u00f3pico, que se han mostrado m\u00e1s profundos que los ya conocidos en el contexto de la teor\u00eda cl\u00e1sica. Las t\u00e9cnicas empleadas van desde el estudio de propiedades de medidas isotr\u00f3picas hasta estimaciones finas de series trigonom\u00e9tricas.  3,- se aborda el estudio de desigualdades inversas en el contexto de la teor\u00eda dual de brunn-minkowski, obteniendose diferentes resultados que permiten inerconectar las desigualdades inversas con problemas cl\u00e1sicos del an\u00e1lisis convexo, hasta tal punto que se prueba que la existencia de determinadas desigualdades inversas es quivalente a la validez de las conjeturas del hiperpalno y de bourgain. Las t\u00e9cnicas empleadas usan distintas herramientas fundamentales del an\u00e1lisis convexo, como la isotrop\u00eda, posiciones de m\u00e1ximo volumen o mm*-estimaciones.  4,- se profundiza en el estudio de la conjetura de vaaler para los conjuntos bpn (1&lt;p&lt;2), prob\u00e1ndose su validez para subespacios de dimensi\u00f3n peque\u00f1a. las t\u00e9cnias emple<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Problemas sobre an\u00e1lisis geom\u00e9trico convexo<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Problemas sobre an\u00e1lisis geom\u00e9trico convexo <\/li>\n<li><strong>Autor:<\/strong>\u00a0  Romance Del R\u00edo Miguel <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Zaragoza<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 24\/05\/2002<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Jes\u00fas Bastero Eleizalde<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Antonio Cordoba barba <\/li>\n<li>Rafael Pay\u00e1 albert (vocal)<\/li>\n<li>Luis m. Arias de reyna Martinez (vocal)<\/li>\n<li> Ru\u00edz blasco Francisco Jos\u00e9 (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Romance Del R\u00edo Miguel El objetivo fundamental de esta tesis es el estudio de dos conceptos b\u00e1sicos [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[3564,3183,32592,126,13610],"tags":[6341,28926,2109,3389,53502,53503],"class_list":["post-17028","post","type-post","status-publish","format-standard","hentry","category-algebras-y-espacios-de-banach","category-analisis-y-analisis-funcional","category-convexidad-y-desigualdades","category-matematicas","category-zaragoza","tag-antonio-cordoba-barba","tag-jesus-bastero-eleizalde","tag-luis-m-arias-de-reyna-Martinez","tag-rafael-paya-albert","tag-romance-del-rio-miguel","tag-ruiz-blasco-francisco-jose"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/17028","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=17028"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/17028\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=17028"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=17028"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=17028"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}