{"id":"https://openalex.org/W2076880061","doi":"https://doi.org/10.1080/10586458.1995.10504305","title":"Higher-Genus Chen\u2013Gackstatter Surfaces and The Weierstrass Representation for Surfaces of Infinite Genus","display_name":"Higher-Genus Chen\u2013Gackstatter Surfaces and The Weierstrass Representation for Surfaces of Infinite Genus","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W2076880061","doi":"https://doi.org/10.1080/10586458.1995.10504305","mag":"2076880061"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.1995.10504305","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.1995.10504305","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049247101","display_name":"Edward C. Thayer","orcid":null},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Edward C. Thayer","raw_affiliation_strings":["Department of Mathematics , University of Massachusetts , 1535 Lederle Graduate Research Center Towers, Amherst , MA , 01003"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Massachusetts , 1535 Lederle Graduate Research Center Towers, Amherst , MA , 01003","institution_ids":["https://openalex.org/I24603500"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049247101"],"corresponding_institution_ids":["https://openalex.org/I24603500"],"apc_list":null,"apc_paid":null,"fwci":1.3568,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.78167316,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"4","issue":"1","first_page":"19","last_page":"39"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7852672338485718},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.7606810331344604},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.668148398399353},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.578035831451416},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.48869040608406067},{"id":"https://openalex.org/keywords/minimal-surface","display_name":"Minimal surface","score":0.4335401654243469},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.42737293243408203},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.42092615365982056},{"id":"https://openalex.org/keywords/chen","display_name":"Chen","score":0.4121472239494324},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4108502268791199},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3612551689147949},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2874571681022644},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25955042243003845},{"id":"https://openalex.org/keywords/zoology","display_name":"Zoology","score":0.08725649118423462},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.07060322165489197}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7852672338485718},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.7606810331344604},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.668148398399353},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.578035831451416},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48869040608406067},{"id":"https://openalex.org/C30707913","wikidata":"https://www.wikidata.org/wiki/Q1545397","display_name":"Minimal surface","level":2,"score":0.4335401654243469},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.42737293243408203},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.42092615365982056},{"id":"https://openalex.org/C2776085556","wikidata":"https://www.wikidata.org/wiki/Q183361","display_name":"Chen","level":2,"score":0.4121472239494324},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4108502268791199},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3612551689147949},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2874571681022644},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25955042243003845},{"id":"https://openalex.org/C90856448","wikidata":"https://www.wikidata.org/wiki/Q431","display_name":"Zoology","level":1,"score":0.08725649118423462},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.07060322165489197},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10586458.1995.10504305","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.1995.10504305","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W76617768","https://openalex.org/W1541637314","https://openalex.org/W1567841374","https://openalex.org/W1742663008","https://openalex.org/W1963952373","https://openalex.org/W1972732705","https://openalex.org/W1978663140","https://openalex.org/W2004659135","https://openalex.org/W2005973282","https://openalex.org/W2030117318","https://openalex.org/W2038386198","https://openalex.org/W2048529987","https://openalex.org/W2060684759","https://openalex.org/W2064124833","https://openalex.org/W2074313127","https://openalex.org/W2076459920","https://openalex.org/W2084475630","https://openalex.org/W2139502098","https://openalex.org/W2171074980","https://openalex.org/W2328695326","https://openalex.org/W4248120324"],"related_works":["https://openalex.org/W2370310922","https://openalex.org/W2386975637","https://openalex.org/W2891436901","https://openalex.org/W2087355708","https://openalex.org/W2388837937","https://openalex.org/W2385339070","https://openalex.org/W2390434941","https://openalex.org/W2385344059","https://openalex.org/W2351657747","https://openalex.org/W2357840119"],"abstract_inverted_index":{"Chen":[0],"and":[1,17,63,70,89,111],"Gackstatter":[2],"(1982)":[3],"constructed":[4],"two":[5],"complete":[6],"minimal":[7,57,128],"surfacesof":[8,98],"finite":[9],"total":[10],"curvature,":[11],"each":[12,82],"having":[13],"one":[14],"Ennepertype":[15],"end":[16],"all":[18],"the":[19,27,32,36,45,68,71,75,120],"symmetries":[20],"of":[21,35,44,55,74,83,94],"Enneper's":[22],"surface.":[23],"Karcher":[24],"[1989]":[25],"generalized":[26],"genus-one":[28],"surface":[29,48],"by":[30,66],"increasing":[31,67],"winding":[33,72],"order":[34,73],"end.":[37,76],"We":[38,51,104],"prove":[39],"that":[40,59],"a":[41,53],"similar":[42],"generalization":[43],"Chen-Gackstatter":[46],"genus-two":[47],"also":[49,105],"exists.":[50],"describe":[52],"collection":[54],"immersed":[56],"surfaces":[58,65,85],"generalize":[60],"both":[61],"Chen-Gackstatter's":[62],"Karcher's":[64],"genus":[69,99],"The":[77],"period":[78],"problem":[79],"associated":[80],"with":[81],"these":[84,109],"is":[86],"explained":[87],"geometrically,":[88],"we":[90],"present":[91],"numerical":[92,116],"evidence":[93],"its":[95],"solvability":[96],"for":[97,123],"as":[100,102],"high":[101],"35.":[103],"make":[106],"conjectures":[107],"concerning":[108],"surfaces,":[110],"explain":[112],"their":[113],"motivation.":[114],"Our":[115],"resultsled":[117],"us":[118],"to":[119],"Weierstrass":[121],"data":[122],"several":[124],"infinite-genus,":[125],"one-ended,":[126],"periodic":[127],"surfaces.":[129]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}