{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:23:12Z","timestamp":1759335792571,"version":"build-2065373602"},"reference-count":7,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T00:00:00Z","timestamp":1747094400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T00:00:00Z","timestamp":1747094400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2025,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>We prove that two compact subsets of complex space <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathbb {C}^n$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow>\n                      <mml:mi>C<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                  <\/mml:msup>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> with corresponding complex homothetic sections (projections) are complex homothetic. The proof uses a new Helly-type theorem for cosets of closed subgroups of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathbb {S}^1$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow>\n                      <mml:mi>S<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s00454-024-00679-1","type":"journal-article","created":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T09:50:01Z","timestamp":1747129801000},"page":"805-813","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Complex Homothetic Sections and Projections Through a Helly Type Theorem for Cosets of $$\\mathbb {S}^1$$"],"prefix":"10.1007","volume":"74","author":[{"given":"Jorge Luis","family":"Arocha","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Javier","family":"Bracho","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luis","family":"Montejano","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,13]]},"reference":[{"issue":"2","key":"679_CR1","doi-asserted-by":"publisher","first-page":"765","DOI":"10.1007\/s11856-016-1394-6","volume":"215","author":"M Alfonseca","year":"2016","unstructured":"Alfonseca, M., Cordier, M., Ryabogin, D.: On bodies with directly congruent projections and sections. Isr. J. Math. 215(2), 765\u2013799 (2016)","journal-title":"Isr. J. Math."},{"key":"679_CR2","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1007\/s00010-022-00916-z","volume":"97","author":"JL Arocha","year":"2023","unstructured":"Arocha, J.L., Bracho, J., Montejano, L.: Complex ellipsoids and complex symmetry. Aequationes math. 97, 295\u2013306 (2023)","journal-title":"Aequationes math."},{"key":"679_CR3","series-title":"Inverse and Posed Problems Series","doi-asserted-by":"publisher","DOI":"10.1515\/9783110920314","volume-title":"Uniqueness Questions in Reconstruction of Multidimensional Objects from Tomography Type Projection Data","author":"VP Golubyatnikov","year":"2000","unstructured":"Golubyatnikov, V.P.: Uniqueness Questions in Reconstruction of Multidimensional Objects from Tomography Type Projection Data. Inverse and Posed Problems Series, De Gruyter, Utrecht (2000)"},{"key":"679_CR4","doi-asserted-by":"publisher","first-page":"3429","DOI":"10.1016\/j.aim.2012.09.010","volume":"231","author":"D Ryabogin","year":"2012","unstructured":"Ryabogin, D.: On the continual Rubik\u2019s cube. Adv. Math. 231, 3429\u20133444 (2012)","journal-title":"Adv. Math."},{"key":"679_CR5","volume-title":"Honor of K\u00e1roly Bezdek\u2019s and Egon Schulte\u2019s 60th Birthdays: Springer Proceedings in Mathematics and Statistics","author":"D Ryabogin","year":"2017","unstructured":"Ryabogin, D.: On symmetries of projections and sections of convex bodies. Discrete geometry and symmetry. In: Marston, D.E., Conder, A.D., Weiss, A.I. (eds.) Honor of K\u00e1roly Bezdek\u2019s and Egon Schulte\u2019s 60th Birthdays: Springer Proceedings in Mathematics and Statistics. Springer, Berlin (2017)"},{"key":"679_CR6","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/s10711-017-0234-0","volume":"190","author":"D Ryabogin","year":"2017","unstructured":"Ryabogin, D.: On a functional equation related to convex bodies with SU(2)-congruent projections. Geom. Dedicata 190, 151\u2013156 (2017)","journal-title":"Geom. Dedicata"},{"key":"679_CR7","first-page":"99","volume":"24","author":"CA Rogers","year":"1965","unstructured":"Rogers, C.A.: Sections and projections of convex bodies. Port. Math. 24, 99\u2013103 (1965)","journal-title":"Port. Math."}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-024-00679-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-024-00679-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-024-00679-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T07:58:43Z","timestamp":1759305523000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-024-00679-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,13]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,10]]}},"alternative-id":["679"],"URL":"https:\/\/doi.org\/10.1007\/s00454-024-00679-1","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2025,5,13]]},"assertion":[{"value":"10 October 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 June 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 June 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 May 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}