{"id":"https://openalex.org/W3134354226","doi":"https://doi.org/10.1137/19m1292989","title":"On Novel Geometric Structures of Laplacian Eigenfunctions in $\\mathbb{R}^3$ and Applications to Inverse Problems","display_name":"On Novel Geometric Structures of Laplacian Eigenfunctions in $\\mathbb{R}^3$ and Applications to Inverse Problems","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3134354226","doi":"https://doi.org/10.1137/19m1292989","mag":"3134354226"},"language":"en","primary_location":{"id":"doi:10.1137/19m1292989","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1292989","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://scholars.cityu.edu.hk/en/publications/on-novel-geometric-structures-of-laplacian-eigenfunctions-in-%E2%84%9Dsup","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064575958","display_name":"Xinlin Cao","orcid":"https://orcid.org/0009-0000-1752-9590"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xinlin Cao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009395387","display_name":"Huaian Diao","orcid":"https://orcid.org/0000-0002-3787-9608"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huaian Diao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025082141","display_name":"Hongyu Liu","orcid":"https://orcid.org/0000-0002-2930-3510"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hongyu Liu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090609331","display_name":"Jun Zou","orcid":"https://orcid.org/0000-0002-4809-7724"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jun Zou","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5064575958"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.6713,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.98880903,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"53","issue":"2","first_page":"1263","last_page":"1294"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.8834735155105591},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.77489173412323},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.6977959871292114},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6581121683120728},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5826111435890198},{"id":"https://openalex.org/keywords/inverse-scattering-problem","display_name":"Inverse scattering problem","score":0.49729087948799133},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4713144898414612},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.44869306683540344},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.42525532841682434},{"id":"https://openalex.org/keywords/identifiability","display_name":"Identifiability","score":0.42133718729019165},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1728512942790985},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08038285374641418}],"concepts":[{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.8834735155105591},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.77489173412323},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6977959871292114},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6581121683120728},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5826111435890198},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.49729087948799133},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4713144898414612},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.44869306683540344},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.42525532841682434},{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.42133718729019165},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1728512942790985},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08038285374641418},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/19m1292989","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1292989","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/on-novel-geometric-structures-of-laplacian-eigenfunctions-in-%E2%84%9Dsup","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/491563ff-24a0-40c8-84c1-a9b38c710564","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/491563ff-24a0-40c8-84c1-a9b38c710564","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CAO, X, DIAO, H, LIU, H & ZOU, J 2021, 'ON NOVEL GEOMETRIC STRUCTURES OF LAPLACIAN EIGENFUNCTIONS IN \u211d 3 AND APPLICATIONS TO INVERSE PROBLEMS', SIAM Journal on Mathematical Analysis, vol. 53, no. 2, pp. 1263-1294. https://doi.org/10.1137/19M1292989","raw_type":"article"}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/on-novel-geometric-structures-of-laplacian-eigenfunctions-in-%E2%84%9Dsup","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3084863313","display_name":null,"funder_award_id":"2412017FZ007","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W175719039","https://openalex.org/W1516032593","https://openalex.org/W1884845041","https://openalex.org/W1969783314","https://openalex.org/W1977207968","https://openalex.org/W2047319386","https://openalex.org/W2049692977","https://openalex.org/W2065245380","https://openalex.org/W2104898428","https://openalex.org/W2135594628","https://openalex.org/W2899964107","https://openalex.org/W2963645054","https://openalex.org/W2963706075","https://openalex.org/W2963799722","https://openalex.org/W3087786811","https://openalex.org/W3089010548","https://openalex.org/W3102334406","https://openalex.org/W3114459875","https://openalex.org/W4245515027"],"related_works":["https://openalex.org/W4302419125","https://openalex.org/W2766128145","https://openalex.org/W2038878154","https://openalex.org/W121031341","https://openalex.org/W2406930625","https://openalex.org/W4300623652","https://openalex.org/W4290982745","https://openalex.org/W2111271529","https://openalex.org/W2464780829","https://openalex.org/W2963746646"],"abstract_inverted_index":{"This":[0],"is":[1,75,121,127],"a":[2,46,149,154,170],"continuation":[3],"and":[4,26,61,95,125,156,173],"an":[5,59,137,167],"extension":[6],"of":[7,23,41,68,81,100,133,143,159,166,177,203],"our":[8],"recent":[9],"work":[10],"[J.":[11],"Math.":[12],"Pures":[13],"Appl.,":[14],"143":[15],"(2020),":[16],"pp.":[17],"116--161]":[18],"on":[19],"the":[20,38,42,65,69,72,79,82,97,101,115,118,128,131,141,160,163,174,188,199,205,210,216],"geometric":[21,119,175,183,200],"structures":[22],"Laplacian":[24,43,102],"eigenfunctions":[25,44,103],"their":[27],"applications":[28],"to":[29,78,191],"inverse":[30,201],"scattering":[31,218],"problems.":[32],"In":[33,85],"that":[34,64,178],"work,":[35],"we":[36,88,186],"studied":[37],"analytic":[39,98,164],"behavior":[40],"at":[45,71,104,169],"point":[47,74,172],"where":[48,106],"two":[49,134],"nodal":[50,107],"or":[51,108],"generalized":[52,109],"singular":[53,110],"lines":[54],"intersect.":[55,112],"The":[56],"results":[57,190,197],"reveal":[58],"important":[60],"intriguing":[62],"property":[63],"vanishing":[66],"order":[67],"eigenfunction":[70,168],"intersecting":[73,83],"closely":[76],"related":[77],"rationality":[80],"angle.":[84],"this":[86,90],"paper,":[87],"continue":[89],"development":[91],"in":[92],"three":[93,146],"dimensions":[94],"study":[96],"behaviors":[99,165],"places":[105],"planes":[111,135,147],"Compared":[113],"with":[114],"two-dimensional":[116],"case,":[117],"situation":[120],"much":[122],"more":[123,144],"complicated,":[124],"so":[126],"corresponding":[129],"analysis:":[130],"intersection":[132,142],"generates":[136,148],"edge":[138],"corner,":[139],"whereas":[140],"than":[145],"vertex":[150],"corner.":[151],"We":[152],"provide":[153],"systematic":[155],"comprehensive":[157],"characterization":[158],"relations":[161],"between":[162],"corner":[171,179],"quantities":[176],"for":[180,198],"all":[181],"these":[182],"cases.":[184],"Moreover,":[185],"apply":[187],"spectral":[189],"establish":[192],"some":[193],"novel":[194],"unique":[195],"identifiability":[196],"problems":[202],"recovering":[204],"shape":[206],"as":[207,209],"well":[208],"(possible)":[211],"surface":[212],"impedance":[213],"coefficient":[214],"by":[215],"associated":[217],"far-field":[219],"measurements.":[220]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-07T14:57:38.498316","created_date":"2025-10-10T00:00:00"}