{"id":157,"date":"2017-09-22T12:46:15","date_gmt":"2017-09-22T15:46:15","guid":{"rendered":"http:\/\/www.professores.uff.br\/almaraz\/?p=157"},"modified":"2025-03-04T07:23:50","modified_gmt":"2025-03-04T10:23:50","slug":"pesquisaresearch","status":"publish","type":"post","link":"https:\/\/www.professores.uff.br\/almaraz\/2017\/09\/22\/pesquisaresearch\/","title":{"rendered":"Research \/ Pesquisa"},"content":{"rendered":"<h4>My research interests are mainly in Differential Geometry and its relationship with Partial Differential Equations, including conformal deformations of Riemannan manifolds and General Relativity.<\/h4>\n<h4 align=\"left\"><em>My publications and preprints:<\/em><\/h4>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>\n<h5>Rigidity of non-compact static domains in hyperbolic space via positive mass theorems (with Levi de Lima), to appear on <em>Annali della Scuola Normale Superiore di Pisa (Classe di Scienze), https:\/\/doi.org\/10.2422\/2036-2145.202301_005<\/em>\u00a0<a href=\"https:\/\/arxiv.org\/pdf\/2206.09768.pdf\">.pdf<\/a><\/h5>\n<\/li>\n<li>A priori estimates for negative constant scalar curvature conformal metrics with positive constant boundary mean curvature (with Shaodong Wang), Journal of the London Mathematical Society, 111:3 (2025), e70109. <em>https:\/\/doi.org\/10.1112\/jlms.70109<\/em><\/li>\n<li>A compactness theorem for conformal metrics with constant scalar curvature and constant boundary mean curvature in dimension three (with Shaodong Wang), Calc. Var. PDEs,<em style=\"color: inherit;font-size: 1em;font-weight: 600\">\u00a0<\/em>64, 35 (2025). <em>https:\/\/doi.org\/10.1007\/s00526-024-02895-2<\/em><\/li>\n<li>\n<h5>A singular Yamabe problem on manifolds with solid cones (with Juan Alcon Apaza), <em>Advances in Calculus of Variations, 17 (2024) 1131-1160. https:\/\/doi.org\/10.1515\/acv-2022-0105<\/em> <a href=\"https:\/\/arxiv.org\/pdf\/2203.13385.pdf\">.pdf<\/a><\/h5>\n<\/li>\n<li>\n<h5>Mass, center of mass and isoperimetry in asymptotically flat 3-manifolds (with Levi de Lima), <em>Calc. Var. PDEs, 62 (2023), 196, https:\/\/doi.org\/10.1007\/s00526-023-02519-1<\/em> <a href=\"https:\/\/arxiv.org\/pdf\/2007.10920.pdf\">.pdf<\/a><\/h5>\n<\/li>\n<li>\n<h5>Energy bounds of sign-changing solutions to Yamabe equations on manifolds with boundary (with Shaodong Wang), <em>Nonlinear Analysis, 225 (2022), 113131, https:\/\/doi.org\/10.1016\/j.na.2022.113131<\/em> <a href=\"https:\/\/arxiv.org\/pdf\/2205.06588.pdf\">.pdf<\/a><\/h5>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>Spacetime positive mass theorems for initial data sets with noncompact boundary (with Levi de Lima and Luciano Mari). <em>International Mathematics Research Notices<\/em>,<em> 2021:4 (2021) 2783\u20132841, https:\/\/doi.org\/10.1093\/imrn\/rnaa226 <a href=\"https:\/\/arxiv.org\/pdf\/1907.02023.pdf\">.pdf<\/a><\/em><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>The mass of an asymptotically hyperbolic manifold with a noncompact boundary (with Levi de Lima). <em>Annales Henri Poincar\u00e9<\/em>, <em>21:11 (2020) 3727-3756, https:\/\/doi.org\/10.1007\/s00023-020-00954-w<\/em> <em><a href=\"https:\/\/www.dropbox.com\/s\/9smq0858ceg0yib\/mass-hyp-bd-AHPO%20%28revised%20version%29.pdf?dl=0\">.pdf<\/a><\/em><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>Convergence of the Yamabe flow on manifolds with minimal boundary (with Liming Sun). <em>Annali della Scuola Normale Superiore di Pisa (Classe di Scienze), 20:3 (2020) 1197-1272, https:\/\/doi.org\/10.2422\/2036-2145.201608_001<\/em>\u00a0<em><a href=\"https:\/\/arxiv.org\/pdf\/1604.06789.pdf\">.pdf<\/a><\/em><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>A compactness theorem for scalar-flat metrics on 3-manifolds with boundary (with Olivaine de Queiroz and Shaodong Wang). <em>Journal of Functional Analysis 277:7 (2019) 2092-2116, https:\/\/doi.org\/10.1016\/j.jfa.2019.01.001<\/em>\u00a0 <em><a href=\"https:\/\/www.dropbox.com\/s\/vfgcy7ykolkk6ru\/Comp_dim3%20-%20final%20version.pdf?dl=0\">.pdf<\/a><\/em><\/li>\n<li>A remark on an eigenvalue problem with mixed boundary condition (with Ezequiel Barbosa). pre-print <a href=\"https:\/\/www.dropbox.com\/s\/ly3vsatqcf4frmb\/Mixed%20boundary.pdf?dl=0\">.pdf<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>A positive mass theorem for asymptotically flat manifolds with a non-compact boundary (with Ezequiel Barbosa and Levi de Lima). <em>Commun. Anal. Geom., 24:4 (2016) 673-715, https:\/\/dx.doi.org\/10.4310\/CAG.2016.v24.n4.a1<\/em>\u00a0<em><a href=\"http:\/\/www.professores.uff.br\/almaraz\/wp-content\/uploads\/sites\/140\/2017\/09\/62014-09-23_body-mass_v2_arxiv.pdf\">.pdf\u00a0<\/a><\/em><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>Convergence of scalar-flat metrics on manifolds with boundary under a Yamabe-type flow. <em>Journal of Diff. Equations, 259 (2015)\u00a0 2626-2694\u00a0<\/em><a href=\"http:\/\/www.professores.uff.br\/almaraz\/wp-content\/uploads\/sites\/140\/2017\/09\/52015-08-05_Yamabe_flow_versao_site_e_arxiv.pdf\"><em>.pdf\u00a0 <\/em><\/a>(Appendix B of this version contains more details than the published one.)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>The asymptotic behavior of Palais-Smale sequences on manifolds with boundary, <em>Pacific J. Math., 269:1 (2014) 1-17<\/em><em>\u00a0<\/em><em><a href=\"http:\/\/www.professores.uff.br\/almaraz\/wp-content\/uploads\/sites\/140\/2017\/09\/4PS_sequences_05-07-15_versao_site_e_arXiv.pdf\">.pdf<\/a><\/em><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>Blow-up phenomena for scalar-flat metrics on manifolds with boundary,\u00a0<em>Journal of Diff. Equations, 251 (2011)\u00a01813-1840 <a href=\"http:\/\/www.professores.uff.br\/almaraz\/wp-content\/uploads\/sites\/140\/2017\/09\/3Loss_Comp_30-04-11_versao_Arxiv_e_site.pdf\">.pdf<\/a><\/em>\u00a0 (This is a more detailed version.)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>A compactness theorem for scalar-flat metrics on manifolds with boundary,\u00a0<em>Calc. Var. PDEs, 41:3 (2011) 341-386 <a href=\"http:\/\/www.meusiteantigo.uff.br\/almaraz\/images\/stories\/Papers\/Arxiv_Compactness_v3_14-12-10.pdf\">.<\/a><a href=\"http:\/\/www.professores.uff.br\/almaraz\/wp-content\/uploads\/sites\/140\/2017\/09\/2Arxiv_Compactness_v3_14-12-10.pdf\">pdf<\/a><\/em><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>An existence theorem of conformal scalar-flat metrics on manifolds with boundary,\u00a0<em>Pacific J. Math. 248:1 (2010) 1-22 <\/em><a href=\"http:\/\/www.meusiteantigo.uff.br\/almaraz\/images\/stories\/Papers\/exist_20-01-10_versao_site.pdf\">.<\/a><a href=\"http:\/\/www.professores.uff.br\/almaraz\/wp-content\/uploads\/sites\/140\/2017\/09\/1exist_20-01-10_versao_site.pdf\">pdf<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<h4 class=\"wp-block-heading\"><em>Some talks I presented:<\/em><\/h4>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">&#8220;Teoremas de massa positiva e problemas do tipo Yamabe&#8221; (in Portuguese). Semin\u00e1rio de EDP e Matem\u00e1tica Aplicada,  <a href=\"https:\/\/www.youtube.com\/watch?v=mZRl7ECSr9E\">video<\/a><\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">&#8220;Spacetime positive mass theorems for initial data sets with noncompact boundary&#8221;.  Workshop on Submanifold Theory and Geometric Analysis. Universidade Federal de S\u00e3o Carlos (Brazil), 2019: <a href=\"https:\/\/www.dropbox.com\/s\/amud98y82j1cx0f\/Talk%20Sao%20Carlos.mp4?dl=0\">video<\/a><\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">&#8220;The mass of asymptotically hyperbolic manifolds with non-compact boundary&#8221;. 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Taipei (Taiwan), 2018: <a href=\"https:\/\/www.dropbox.com\/s\/rppk5lm37yojmjv\/2018-07-08%20Taipei.pdf?dl=0\"> slides<\/a><\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">&#8220;On Yamabe-type problems on manifolds with boundary&#8221;.   Mathematical Congress of the Americas (MCA),  Montreal (Canada), 2017:  <a href=\"https:\/\/www.dropbox.com\/s\/yw9hrxxtnr7tppj\/2017-07-27%20MCA%20Montreal.pdf?dl=0\">slides<\/a> ; 31st Brazilian Mathematics Colloquium, IMPA, Rio de Janeiro (Brazil), 2017: <a href=\"https:\/\/www.youtube.com\/watch?v=FRUn4CQZq6Q&amp;t=2051s\">video<\/a><\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">&#8220;Convergence of the Yamabe flow on manifolds with minimal boundary&#8221;.<br>VI Workshop on Differential Geometry,  Macei\u00f3 (Brazil), 2016: <a href=\"https:\/\/www.dropbox.com\/s\/0kdb8kx5nhav564\/00008.MTS?dl=0\">video part 1<\/a> , <a href=\"https:\/\/www.dropbox.com\/s\/0uzbojgp66nd9uq\/00009.MTS?dl=0\">video part 2 <\/a><\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">&#8220;A positive mass theorem for asymptotically flat manifolds with a noncompact boundary and an application to a Yamabe-type flow&#8221;.<br>Differential Geometry &amp; Geometric Analysis Seminar, Princeton University (USA), 2015:  <a href=\"https:\/\/www.dropbox.com\/s\/xwywhemfgzjhnri\/2015-01-20%20Princeton.pdf?dl=0\">slides<\/a><\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">&#8220;Convergence of a Yamabe-type flow for manifolds with boundary&#8221;. Second Pacific Rim Mathematical Association Congress (PRIMA), Shanghai (China), 2013: <a href=\"https:\/\/www.dropbox.com\/s\/pb080xk1kae6iou\/2013-06-27%20PRIMA.pdf?dl=0\">slides<\/a><\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">&#8220;The set of conformal scalar-flat metrics on manifolds with boundary: compactness and noncompactness results&#8221;. 28th Brazilian Mathematics Colloquium, IMPA, Rio de Janeiro (Brazil), 2011: <a href=\"https:\/\/www.dropbox.com\/s\/25zw62odt90hfcy\/Coloquio_23-07-2011.pdf?dl=0\">slides<\/a><br><\/h4>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>My research interests are mainly in Differential Geometry and its relationship with Partial Differential Equations, including conformal deformations of Riemannan manifolds and General Relativity. My publications and preprints: Rigidity of non-compact static domains in hyperbolic space via positive mass theorems (with Levi de Lima), to appear on Annali della Scuola Normale Superiore di Pisa (Classe [&hellip;]<\/p>\n","protected":false},"author":146,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[3],"tags":[],"class_list":["post-157","post","type-post","status-publish","format-standard","hentry","category-pesquisas"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/almaraz\/wp-json\/wp\/v2\/posts\/157","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.professores.uff.br\/almaraz\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.professores.uff.br\/almaraz\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/almaraz\/wp-json\/wp\/v2\/users\/146"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/almaraz\/wp-json\/wp\/v2\/comments?post=157"}],"version-history":[{"count":76,"href":"https:\/\/www.professores.uff.br\/almaraz\/wp-json\/wp\/v2\/posts\/157\/revisions"}],"predecessor-version":[{"id":450,"href":"https:\/\/www.professores.uff.br\/almaraz\/wp-json\/wp\/v2\/posts\/157\/revisions\/450"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/almaraz\/wp-json\/wp\/v2\/media?parent=157"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/almaraz\/wp-json\/wp\/v2\/categories?post=157"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/almaraz\/wp-json\/wp\/v2\/tags?post=157"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}