{"paper":{"title":"Harmonic Close-to-convex Functions and Minimal Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"A. Rasila, A. Sairam Kaliraj, S. Ponnusamy","submitted_at":"2012-09-02T19:03:37Z","abstract_excerpt":"In this paper, we study the family ${\\mathcal C}_{H}^0$ of sense-preserving complex-valued harmonic functions $f$ that are normalized close-to-convex functions on the open unit disk $\\mathbb{D}$ with $f_{\\bar{z}}(0)=0$. We derive a sufficient condition for $f$ to belong to the class $\\CC_{H}^0$. We take the analytic part of $f$ to be $zF(a,b;c;z)$ or $zF(a,b;c;z^2)$ and for a suitable choice of co-analytic part of $f$, the second complex dilatation $w(z)=\\bar{f_{\\bar{z}}}/f_z$ turns out to be a square of an analytic function. Hence $f$ is lifted to a minimal surface expressed by an isothermal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0202","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":""},"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"}