{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,9]],"date-time":"2025-11-09T07:38:08Z","timestamp":1762673888658},"reference-count":7,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:p>Given a collection of minimal graphs,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:msub><mml:mi>M<\/mml:mi><mml:mn>1<\/mml:mn><\/mml:msub><mml:mo>,<\/mml:mo><mml:msub><mml:mi>M<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msub><mml:mo>,<\/mml:mo><mml:mo>\u2026<\/mml:mo><mml:mo>,<\/mml:mo><mml:msub><mml:mi>M<\/mml:mi><mml:mi>n<\/mml:mi><\/mml:msub><\/mml:math>, with isothermal parametrizations in terms of the Gauss map and height differential, we give sufficient conditions on<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:msub><mml:mi>M<\/mml:mi><mml:mn>1<\/mml:mn><\/mml:msub><mml:mo>,<\/mml:mo><mml:msub><mml:mi>M<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msub><mml:mo>,<\/mml:mo><mml:mo>\u2026<\/mml:mo><mml:mo>,<\/mml:mo><mml:msub><mml:mi>M<\/mml:mi><mml:mi>n<\/mml:mi><\/mml:msub><\/mml:math>so that a convex combination of them will be a minimal graph. We will then provide two examples, taking a convex combination of Scherk's doubly periodic surface with the catenoid and Enneper's surface, respectively.<\/jats:p>","DOI":"10.1155\/2012\/724268","type":"journal-article","created":{"date-parts":[[2012,8,15]],"date-time":"2012-08-15T21:01:02Z","timestamp":1345064462000},"page":"1-9","source":"Crossref","is-referenced-by-count":1,"title":["Convex Combinations of Minimal Graphs"],"prefix":"10.1155","volume":"2012","author":[{"given":"Michael","family":"Dorff","sequence":"first","affiliation":[{"name":"Department of Mathematics, Brigham Young University, Provo, UT 84602, USA"}]},{"given":"Ryan","family":"Viertel","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Brigham Young University, Provo, UT 84602, USA"}]},{"given":"Magdalena","family":"Wo\u0142oszkiewicz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Maria Curie-Sklodowska University, 20-031 Lublin, Poland"}]}],"member":"98","reference":[{"key":"4","first-page":"197","volume-title":"Anamorphosis, mapping problems, and harmonic univalent functions","year":"2012"},{"key":"1"},{"key":"2","first-page":"3","volume":"9","year":"1984","journal-title":"Annales Academiae Scientiarum Fennicae"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1936-06397-4"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546600"},{"key":"9","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF02567334","volume":"45","year":"1970","journal-title":"Commentarii Mathematici Helvetici"},{"issue":"1","key":"12","doi-asserted-by":"crossref","first-page":"115","DOI":"10.4310\/jdg\/1214442162","volume":"28","year":"1988","journal-title":"Journal of Differential Geometry"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/724268.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/724268.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/724268.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,20]],"date-time":"2017-06-20T22:53:52Z","timestamp":1497999232000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ijmms\/2012\/724268\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"references-count":7,"alternative-id":["724268","724268"],"URL":"https:\/\/doi.org\/10.1155\/2012\/724268","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012]]}}}