{"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"abstract":[{"text":"In this paper we prove several new results around Gromov's waist theorem. We give a simple proof of Vaaler's theorem on sections of the unit cube using the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective spaces, flat tori, convex bodies in Euclidean space; and establish waist-type results in terms of the Hausdorff measure.","lang":"eng"}],"scopus_import":"1","quality_controlled":"1","department":[{"_id":"HeEd"}],"citation":{"ista":"Akopyan A, Hubard A, Karasev R. 2019. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 53(2), 457–490.","ama":"Akopyan A, Hubard A, Karasev R. Lower and upper bounds for the waists of different spaces. <i>Topological Methods in Nonlinear Analysis</i>. 2019;53(2):457-490. doi:<a href=\"https://doi.org/10.12775/TMNA.2019.008\">10.12775/TMNA.2019.008</a>","short":"A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490.","chicago":"Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds for the Waists of Different Spaces.” <i>Topological Methods in Nonlinear Analysis</i>. Akademicka Platforma Czasopism, 2019. <a href=\"https://doi.org/10.12775/TMNA.2019.008\">https://doi.org/10.12775/TMNA.2019.008</a>.","mla":"Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different Spaces.” <i>Topological Methods in Nonlinear Analysis</i>, vol. 53, no. 2, Akademicka Platforma Czasopism, 2019, pp. 457–90, doi:<a href=\"https://doi.org/10.12775/TMNA.2019.008\">10.12775/TMNA.2019.008</a>.","apa":"Akopyan, A., Hubard, A., &#38; Karasev, R. (2019). Lower and upper bounds for the waists of different spaces. <i>Topological Methods in Nonlinear Analysis</i>. Akademicka Platforma Czasopism. <a href=\"https://doi.org/10.12775/TMNA.2019.008\">https://doi.org/10.12775/TMNA.2019.008</a>","ieee":"A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists of different spaces,” <i>Topological Methods in Nonlinear Analysis</i>, vol. 53, no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019."},"intvolume":"        53","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"full_name":"Hubard, Alfredo","last_name":"Hubard","first_name":"Alfredo"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}],"isi":1,"title":"Lower and upper bounds for the waists of different spaces","ec_funded":1,"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","date_published":"2019-06-01T00:00:00Z","oa_version":"Preprint","date_created":"2019-07-14T21:59:19Z","month":"06","type":"journal_article","_id":"6634","publication":"Topological Methods in Nonlinear Analysis","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.06926"}],"date_updated":"2023-08-29T06:32:48Z","page":"457-490","doi":"10.12775/TMNA.2019.008","issue":"2","external_id":{"arxiv":["1612.06926"],"isi":["000472541600004"]},"publication_status":"published","oa":1,"language":[{"iso":"eng"}],"day":"01","publisher":"Akademicka Platforma Czasopism","year":"2019","volume":53}