{"id":"https://openalex.org/W4416055631","doi":"https://doi.org/10.1007/s00454-025-00751-4","title":"Rolling Spheres and the Willmore Energy","display_name":"Rolling Spheres and the Willmore Energy","publication_year":2025,"publication_date":"2025-11-09","ids":{"openalex":"https://openalex.org/W4416055631","doi":"https://doi.org/10.1007/s00454-025-00751-4"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-025-00751-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-025-00751-4","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","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/A5050706780","display_name":"Felix Kn\u00f6ppel","orcid":"https://orcid.org/0000-0002-0191-2859"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Felix Kn\u00f6ppel","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029151317","display_name":"Ulrich Pinkall","orcid":"https://orcid.org/0000-0002-2087-6435"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ulrich Pinkall","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051948556","display_name":"Peter Schr\u00f6der","orcid":"https://orcid.org/0000-0001-9084-7106"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Peter Schr\u00f6der","raw_affiliation_strings":["Hausdorff Center for Mathematics, University of Bonn, Bonn, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hausdorff Center for Mathematics, University of Bonn, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044759674","display_name":"Yousuf Soliman","orcid":"https://orcid.org/0000-0003-4023-5026"},"institutions":[{"id":"https://openalex.org/I4210144001","display_name":"Crosslight Software (Canada)","ror":"https://ror.org/03vfany12","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210144001"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Yousuf Soliman","raw_affiliation_strings":["Side Effects Software, Toronto, Canada"],"raw_orcid":"https://orcid.org/0000-0003-4023-5026","affiliations":[{"raw_affiliation_string":"Side Effects Software, Toronto, Canada","institution_ids":["https://openalex.org/I4210144001"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044759674"],"corresponding_institution_ids":["https://openalex.org/I4210144001"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":2.2721,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.89116461,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"76","issue":"1","first_page":"177","last_page":"218"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.5353999733924866,"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":0.5353999733924866,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.22579999268054962,"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":0.037300001829862595,"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/willmore-energy","display_name":"Willmore energy","score":0.9193000197410583},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6769000291824341},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.6662999987602234},{"id":"https://openalex.org/keywords/conformal-map","display_name":"Conformal map","score":0.6560999751091003},{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.6287000179290771},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5856999754905701},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.47099998593330383},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.43230000138282776}],"concepts":[{"id":"https://openalex.org/C39428390","wikidata":"https://www.wikidata.org/wiki/Q2581692","display_name":"Willmore energy","level":5,"score":0.9193000197410583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6830999851226807},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6769000291824341},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6662999987602234},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.6560999751091003},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.6287000179290771},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5856999754905701},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5175999999046326},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.47099998593330383},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4325999915599823},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.43230000138282776},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.3935000002384186},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.33959999680519104},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.3368000090122223},{"id":"https://openalex.org/C153782549","wikidata":"https://www.wikidata.org/wiki/Q175116","display_name":"Discrete space","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C16063025","wikidata":"https://www.wikidata.org/wiki/Q4370338","display_name":"Total curvature","level":5,"score":0.3292999863624573},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.32519999146461487},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3133000135421753},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.2590999901294708}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-025-00751-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-025-00751-4","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7925834365","display_name":null,"funder_award_id":"2019279416","funder_id":"https://openalex.org/F4562087700","funder_display_name":"National Science Foundation Graduate Research Fellowship Program"},{"id":"https://openalex.org/G822936381","display_name":"TRR 109: Diskretisierung in Geometrie und Dynamik","funder_award_id":"195170736","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323688","display_name":"Einstein Stiftung Berlin","ror":"https://ror.org/03s0fv852"},{"id":"https://openalex.org/F4562087700","display_name":"National Science Foundation Graduate Research Fellowship Program","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1484275443","https://openalex.org/W1484918381","https://openalex.org/W1600314051","https://openalex.org/W1606077524","https://openalex.org/W1701606820","https://openalex.org/W1963799857","https://openalex.org/W1987445545","https://openalex.org/W1998249025","https://openalex.org/W2015707217","https://openalex.org/W2035777584","https://openalex.org/W2038460253","https://openalex.org/W2042748670","https://openalex.org/W2067257899","https://openalex.org/W2084986525","https://openalex.org/W2086051335","https://openalex.org/W2105340951","https://openalex.org/W2126411107","https://openalex.org/W2136227852","https://openalex.org/W2264936970","https://openalex.org/W2949521785","https://openalex.org/W2962753345","https://openalex.org/W2963618607","https://openalex.org/W3015227654","https://openalex.org/W3180312704","https://openalex.org/W3197038377","https://openalex.org/W4246121787","https://openalex.org/W4300866069","https://openalex.org/W4389334888","https://openalex.org/W6945349759"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-11-09T00:00:00"}