{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T00:01:50Z","timestamp":1724371310829},"reference-count":28,"publisher":"Oxford University Press (OUP)","issue":"16","license":[{"start":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T00:00:00Z","timestamp":1719964800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,8,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The non-abelian Hodge correspondence maps a polystable $\\textrm{SL}(2, {\\mathbb{R}})$-Higgs bundle on a compact Riemann surface $X$ of genus $g \\geq 2$ to a connection that, in some cases, is the holonomy of a branched hyperbolic structure. Gaiotto\u2019s conformal limit maps the same bundle to a partial oper, that is, to a connection whose holonomy is that of a branched complex projective structure compatible with $X$. In this article, we show how these are both instances of the same phenomenon: the family of connections appearing in the conformal limit can be understood as a family of complex projective structures, deforming the hyperbolic ones into the ones compatible with $X$. We also show that, for zero Toledo invariant, this deformation is optimal, inducing a geodesic on Teichm\u00fcller\u2019s space.<\/jats:p>","DOI":"10.1093\/imrn\/rnae142","type":"journal-article","created":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T09:23:59Z","timestamp":1719998639000},"page":"11812-11831","source":"Crossref","is-referenced-by-count":0,"title":["The Conformal Limit and Projective Structures"],"prefix":"10.1093","volume":"2024","author":[{"given":"Pedro","family":"M Silva","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica da Universidade do Porto , Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias da Universidade do Porto, Rua do Campo Alegre s\/n, 4169-007 Porto, Portugal"}]},{"given":"Peter B","family":"Gothen","sequence":"additional","affiliation":[{"name":"Centro de Matem\u00e1tica da Universidade do Porto , Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias da Universidade do Porto, Rua do Campo Alegre s\/n, 4169-007 Porto, Portugal"}]}],"member":"286","published-online":{"date-parts":[[2024,7,3]]},"reference":[{"article-title":"Projective structures with (quasi-) Hitchin holonomy","year":"2021","author":"Alessandrini","key":"2024082208014372600_ref1"},{"key":"2024082208014372600_ref2","article-title":"Higgs bundles and geometric structures on manifolds","volume":"15","author":"Alessandrini","year":"2019","journal-title":"SIGMA Symmetry Integrability Geom. 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