{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T10:48:43Z","timestamp":1772275723886,"version":"3.50.1"},"reference-count":18,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2017,8,28]],"date-time":"2017-08-28T00:00:00Z","timestamp":1503878400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The first   author  was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF)","award":["2015R1D1A1A01060046"],"award-info":[{"award-number":["2015R1D1A1A01060046"]}]},{"name":"The fourth author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education","award":["2017R1D1A1B03033978"],"award-info":[{"award-number":["2017R1D1A1B03033978"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Our principal goal is to study the prescribed curvature problem in a manifold with density. In particular, we consider the Euclidean 3-space     R 3     with a positive density function     e \u03d5    , where     \u03d5 = -  x 2  -  y 2     ,      ( x , y , z )  \u2208  R 3      and construct all the helicoidal surfaces in the space by solving the second-order non-linear ordinary differential equation with the weighted Gaussian curvature and the mean curvature functions. As a result, we give a classification of weighted minimal helicoidal surfaces as well as examples of helicoidal surfaces with some weighted Gaussian curvature and mean curvature functions in the space.<\/jats:p>","DOI":"10.3390\/sym9090173","type":"journal-article","created":{"date-parts":[[2017,8,28]],"date-time":"2017-08-28T12:08:37Z","timestamp":1503922117000},"page":"173","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Constructions of Helicoidal Surfaces in Euclidean Space with Density"],"prefix":"10.3390","volume":"9","author":[{"given":"Dae","family":"Yoon","sequence":"first","affiliation":[{"name":"Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dong-Soo","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Chonnam National University, Gwangju 61186, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Young","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kyungpook National University, Daegu 41566, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jae","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"147","DOI":"10.2748\/tmj\/1178229688","article-title":"Surfaces of revolution with prescribed mean curvature","volume":"32","author":"Kenmotsu","year":"1980","journal-title":"T\u00f4hoku Math. 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Math."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/9\/173\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:29Z","timestamp":1760208209000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/9\/173"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,28]]},"references-count":18,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2017,9]]}},"alternative-id":["sym9090173"],"URL":"https:\/\/doi.org\/10.3390\/sym9090173","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,28]]}}}