{"paper":{"title":"Families of proper minimal surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Antonio Alarcon, Franc Forstneric","submitted_at":"2026-05-19T14:14:48Z","abstract_excerpt":"Assume that $X$ is a connected, open, oriented smooth surface, $B$ is a compact Euclidean neighbourhood retract, and $\\mathscr{J}=\\{J_b\\}_{b\\in B}$ is a continuous family of complex structures on $X$ of local H\\\"older class $\\mathscr{C}^\\alpha$ for some $0<\\alpha<1$. We construct a continuous family of $J_b$-conformal minimal immersions $u_b:X\\to \\mathbb{R}^3$, $b\\in B$, properly projecting to $\\mathbb{R}^2$ and having an arbitrary given family of flux homomorphisms ${\\rm Flux}_{u_b}:H_1(X,\\mathbb{Z})\\to\\mathbb{R}^3$. In particular, there are continuous families of proper $J_b$-holomorphic nul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19883","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.19883/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}