{"id":"https://openalex.org/W7206217998","doi":"https://doi.org/10.48550/arxiv.2609.01540","title":"Stability of the Riemannian positive mass theorem in all dimensions","display_name":"Stability of the Riemannian positive mass theorem in all dimensions","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W7206217998","doi":"https://doi.org/10.48550/arxiv.2609.01540"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.01540","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01540","pdf_url":"https://arxiv.org/pdf/2609.01540","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/2609.01540","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152480647","display_name":"Gaoming Wang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Gaoming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101472635","display_name":"Yiyue Zhang","orcid":"https://orcid.org/0000-0002-7694-5786","observed_orcids":["https://orcid.org/0000-0002-7694-5786"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Yiyue","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.001500000013038516,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/asymptotically-flat-manifolds","display_name":"asymptotically flat manifolds","score":0.972000002861023},{"id":"https://openalex.org/keywords/nonnegative-scalar-curvature","display_name":"nonnegative scalar curvature","score":0.9810000061988831},{"id":"https://openalex.org/keywords/adm-mass","display_name":"ADM mass","score":0.9829999804496765},{"id":"https://openalex.org/keywords/excision","display_name":"excision","score":0.4410000145435333},{"id":"https://openalex.org/keywords/minimal-graphs","display_name":"minimal graphs","score":0.9350000023841858},{"id":"https://openalex.org/keywords/global-coordinates","display_name":"global coordinates","score":0.5690000057220459},{"id":"https://openalex.org/keywords/extra-dimensions","display_name":"extra dimensions","score":0.5239999890327454}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7512999773025513},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5182999968528748},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5151000022888184},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.5037000179290771},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.49810001254081726},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.49380001425743103},{"id":"https://openalex.org/C42704618","wikidata":"https://www.wikidata.org/wiki/Q910917","display_name":"Spin (aerodynamics)","level":2,"score":0.48100000619888306},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4726000130176544},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.47099998593330383},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.44200000166893005},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4397999942302704},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4203999936580658},{"id":"https://openalex.org/C155673373","wikidata":"https://www.wikidata.org/wiki/Q1648886","display_name":"Structural stability","level":2,"score":0.4129999876022339},{"id":"https://openalex.org/C74802450","wikidata":"https://www.wikidata.org/wiki/Q2070474","display_name":"Seven-dimensional space","level":4,"score":0.4002000093460083},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3977999985218048},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.39719998836517334},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.38850000500679016},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.38510000705718994},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.3702999949455261},{"id":"https://openalex.org/C2983854663","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Negative curvature","level":3,"score":0.359499990940094},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.34940001368522644},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.34220001101493835},{"id":"https://openalex.org/C167204820","wikidata":"https://www.wikidata.org/wiki/Q912058","display_name":"Simply connected space","level":2,"score":0.34049999713897705},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C2985318062","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theorem","level":3,"score":0.3140999972820282},{"id":"https://openalex.org/C129049296","wikidata":"https://www.wikidata.org/wiki/Q548675","display_name":"Levi-Civita connection","level":5,"score":0.3095000088214874},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C4306028","wikidata":"https://www.wikidata.org/wiki/Q2185349","display_name":"Fundamental theorem of Riemannian geometry","level":4,"score":0.302700012922287},{"id":"https://openalex.org/C2779396167","wikidata":"https://www.wikidata.org/wiki/Q5156040","display_name":"Comparison theorem","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C88221313","wikidata":"https://www.wikidata.org/wiki/Q203586","display_name":"Poincar\u00e9 conjecture","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C16140857","wikidata":"https://www.wikidata.org/wiki/Q945953","display_name":"Gaussian curvature","level":3,"score":0.26660001277923584},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.265500009059906}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.01540","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01540","pdf_url":"https://arxiv.org/pdf/2609.01540","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.2609.01540","doi":"https://doi.org/10.48550/arxiv.2609.01540","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.01540","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:2609.01540","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01540","pdf_url":"https://arxiv.org/pdf/2609.01540","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7206217998.pdf","grobid_xml":"https://content.openalex.org/works/W7206217998.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4416053752","https://openalex.org/W7152957496","https://openalex.org/W7202201350"],"related_works":["https://openalex.org/W4225966613","https://openalex.org/W2006678947","https://openalex.org/W7165661259","https://openalex.org/W2963435698","https://openalex.org/W2789342663","https://openalex.org/W4405003295","https://openalex.org/W2805260491","https://openalex.org/W4392807520","https://openalex.org/W4298879877","https://openalex.org/W6920503455"],"abstract_inverted_index":{"We":[0],"prove":[1],"stability":[2,15],"of":[3,20,71],"the":[4,13,51,72,77],"Riemannian":[5],"positive":[6],"mass":[7],"theorem":[8],"in":[9,50],"all":[10],"dimensions,":[11],"extending":[12],"Dong-Song":[14],"theorem.":[16],"For":[17],"a":[18],"sequence":[19],"complete":[21],"asymptotically":[22],"flat":[23],"manifolds":[24],"with":[25],"nonnegative":[26],"scalar":[27,69],"curvature":[28],"and":[29,64],"ADM":[30],"masses":[31],"tending":[32],"to":[33,41,47],"zero,":[34],"excising":[35],"domains":[36],"whose":[37],"boundary":[38],"areas":[39],"tend":[40],"zero":[42],"yields":[43],"exterior":[44],"regions":[45],"converging":[46],"Euclidean":[48],"space":[49],"pointed":[52],"measured":[53],"Gromov-Hausdorff":[54],"topology.":[55],"The":[56],"proof":[57],"constructs":[58],"global":[59],"coordinates":[60],"from":[61],"minimal":[62],"graphs":[63],"controls":[65],"their":[66],"Hessians":[67],"using":[68],"solutions":[70],"conformal":[73],"Laplace":[74],"equation":[75],"on":[76],"associated":[78],"graph":[79],"metrics.":[80]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-03T00:00:00"}