{"id":62419,"date":"2018-03-09T22:50:17","date_gmt":"2018-03-09T22:50:17","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/volume-preserving-curvature-flows-in-rotationally-symmetric-spaces\/"},"modified":"2018-03-09T22:50:17","modified_gmt":"2018-03-09T22:50:17","slug":"volume-preserving-curvature-flows-in-rotationally-symmetric-spaces","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/volume-preserving-curvature-flows-in-rotationally-symmetric-spaces\/","title":{"rendered":"Volume preserving curvature flows in rotationally symmetric spaces"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Esther Cabezas Rivas <\/strong><\/h2>\n<p>En la tesis titulada \u00abvolume preserving curvature flows in rotationally symmetric spaces\u00bb se exporta por primera vez a un espacio no llano (en concreto, al espacio hiperb\u00f3lico) un resultado probado por g. Huisken en 1987, seg\u00fan el cual bajo el flujo por la curvatura media preservando vol\u00famenes (vpmcf), las hipersuperficies convexas en el espacio eucl\u00eddeo se mantienen convexas durante toda la evoluci\u00f3n, la cual existe para todo tiempo positivo y la soluci\u00f3n converge exponencialmente a una espera redonda. Con m\u00e1s precisi\u00f3n, en el citado trabajo demostramos teorema 1.  Sea un espacio hiperb\u00f3lico m_l (n + 1)-dimensional, completo, simplemente conexo y de curvatura seccional constante negativa l  menor que  0. Si m0 es una hipersuperficie compacta y convexa por horosferas (h-convexa), entonces vpmcf con condici\u00f3n inicial m0 tiene una soluci\u00f3n \u00fanica mt tal que (i)   est\u00e1 definida para todo tiempo, (ii)  las hipersuperficies m_t permanecen diferenciables y h-convexas para todo tiempo (iii) la soluci\u00f3n converge exponencialmente (cuando t se acerca a infinito, en la topolog\u00eda cm, para cualquier m natural fijo) a una esfera geod\u00e9sica de m_l  incluyendo el mismo volumen que m_0. adem\u00e1s, gracias a la comprensi\u00f3n y adaptaci\u00f3n (al ambiente hiperb\u00f3lico) de la teor\u00eda de regularidad maximal, en la tesis se extienden las afirmaciones (i) y (iii) del teorema 1 a ciertos datos iniciales no necesariamente h-convexos. En concreto, como subproducto de la demostraci\u00f3n de (iii), probamos el siguiente resultado: teorema 2. Sea s una esfera geod\u00e9sica de m_l(n+1) y 0  menor que  b  menor que 1. Existe    mayor que  0 tal que, para cualquier embebimiento x: m &#8212; mayor que  m_l(n+1) con h(1+b)-distancia a s menor que  , el vpmcf tiene una \u00fanica soluci\u00f3n cumpliendo x_0 = x, definida para todo tiempo y que converge exponencialmente a una esfera geod\u00e9sica en m_l(n+1), h(1+b)-pr\u00f3xima a s e incluyendo el mismo volumen que x(m). por otra parte, en esta tesis se export<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Volume preserving curvature flows in rotationally symmetric spaces<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Volume preserving curvature flows in rotationally symmetric spaces <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Esther Cabezas Rivas <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Universitat de val\u00e9ncia (estudi general)<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 16\/01\/2008<\/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> Miquel Molina Vicente Felipe<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Antonio Ros mulero <\/li>\n<li>Manuel Mar\u00eda Ritore cortes (vocal)<\/li>\n<li>gerhard Huisken (vocal)<\/li>\n<li>peter Topping (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Esther Cabezas Rivas En la tesis titulada \u00abvolume preserving curvature flows in rotationally symmetric spaces\u00bb se exporta [&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 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