{"id":"https://openalex.org/W7204102428","doi":"https://doi.org/10.48550/arxiv.2608.21085","title":"Robin and Neumann problems for the graph scalar curvature equation","display_name":"Robin and Neumann problems for the graph scalar curvature equation","publication_year":2026,"publication_date":"2026-08-21","ids":{"openalex":"https://openalex.org/W7204102428","doi":"https://doi.org/10.48550/arxiv.2608.21085"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.21085","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.21085","pdf_url":"https://arxiv.org/pdf/2608.21085","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.21085","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082371563","display_name":"Guohuan Qiu","orcid":"https://orcid.org/0000-0002-2654-4044","observed_orcids":["https://orcid.org/0000-0002-2654-4044"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Qiu, Guohuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5082371563"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9965999722480774,"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":0.9965999722480774,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.0017000000225380063,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.0010000000474974513,"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/robin-boundary-conditions","display_name":"Robin boundary conditions","score":0.6710000038146973},{"id":"https://openalex.org/keywords/neumann-boundary-conditions","display_name":"Neumann boundary conditions","score":0.9810000061988831},{"id":"https://openalex.org/keywords/existence-and-uniqueness-of-solutions","display_name":"existence and uniqueness of solutions","score":0.9120000004768372},{"id":"https://openalex.org/keywords/volume-threshold","display_name":"volume threshold","score":0.5979999899864197},{"id":"https://openalex.org/keywords/three-dimensional-surfaces","display_name":"three-dimensional surfaces","score":0.4230000078678131}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8003000020980835},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.6568999886512756},{"id":"https://openalex.org/C108257041","wikidata":"https://www.wikidata.org/wiki/Q748993","display_name":"Robin boundary condition","level":4,"score":0.5874000191688538},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5830000042915344},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5715000033378601},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5644000172615051},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5340999960899353},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5016000270843506},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.43220001459121704},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.41659998893737793},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.38850000500679016},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.3806000053882599},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.37400001287460327},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.3407999873161316},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.21085","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.21085","pdf_url":"https://arxiv.org/pdf/2608.21085","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.21085","doi":"https://doi.org/10.48550/arxiv.2608.21085","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.21085","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.21085","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.21085","pdf_url":"https://arxiv.org/pdf/2608.21085","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204102428.pdf","grobid_xml":"https://content.openalex.org/works/W7204102428.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1866311589","https://openalex.org/W1965827855","https://openalex.org/W1969826220","https://openalex.org/W1982161647","https://openalex.org/W1982921635","https://openalex.org/W2008381371","https://openalex.org/W2027090993","https://openalex.org/W2029410798","https://openalex.org/W2068067097","https://openalex.org/W2075703498","https://openalex.org/W2079741820","https://openalex.org/W2083309282","https://openalex.org/W2095238990","https://openalex.org/W2123224137","https://openalex.org/W2143305959","https://openalex.org/W2154400073","https://openalex.org/W2228711623","https://openalex.org/W2254297655","https://openalex.org/W2494809215","https://openalex.org/W2761691702","https://openalex.org/W2766975214","https://openalex.org/W2934404753","https://openalex.org/W2948201513","https://openalex.org/W2963647291","https://openalex.org/W2964139817","https://openalex.org/W2964159702","https://openalex.org/W3101076456","https://openalex.org/W4380370822","https://openalex.org/W4392737244","https://openalex.org/W4398792135","https://openalex.org/W4398795020","https://openalex.org/W4406072733","https://openalex.org/W7116951384","https://openalex.org/W7171557740"],"related_works":["https://openalex.org/W7207571619","https://openalex.org/W2036539886","https://openalex.org/W1984046565","https://openalex.org/W2010237800","https://openalex.org/W4403624409","https://openalex.org/W3041133648","https://openalex.org/W6959761323","https://openalex.org/W1972179471","https://openalex.org/W2083882783","https://openalex.org/W2189228246"],"abstract_inverted_index":{"We":[0],"study":[1],"Robin":[2,33,43,71],"and":[3,29,35,75],"Neumann":[4,39],"problems":[5],"for":[6,31],"the":[7,32,42,58,70,81],"scalar":[8],"curvature":[9,77],"equation":[10],"of":[11],"admissible":[12],"graphs":[13],"over":[14],"bounded":[15],"uniformly":[16],"convex":[17],"domains":[18],"in":[19,69],"three":[20],"dimensions.":[21],"Under":[22],"a":[23,37,64],"small-volume":[24],"assumption,":[25],"we":[26],"prove":[27],"existence":[28],"uniqueness":[30],"problem":[34],"obtain":[36],"classical":[38],"solution":[40],"as":[41],"parameter":[44],"tends":[45],"to":[46],"zero.":[47],"The":[48,60],"volume":[49],"threshold":[50],"is":[51,63],"optimal":[52],"among":[53],"conditions":[54],"depending":[55],"only":[56],"on":[57],"volume.":[59],"main":[61],"step":[62],"boundary":[65],"second-derivative":[66],"estimate":[67],"uniform":[68],"parameter;":[72],"known":[73],"interior":[74],"global-to-boundary":[76],"estimates":[78],"then":[79],"give":[80],"global":[82],"bound.":[83]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-25T00:00:00"}
