{"main_file_link":[{"url":"https://arxiv.org/abs/1612.06926","open_access":"1"}],"quality_controlled":"1","scopus_import":"1","title":"Lower and upper bounds for the waists of different spaces","issue":"2","oa_version":"Preprint","intvolume":"        53","language":[{"iso":"eng"}],"publisher":"Akademicka Platforma Czasopism","year":"2019","ec_funded":1,"day":"01","date_published":"2019-06-01T00:00:00Z","_id":"6634","doi":"10.12775/TMNA.2019.008","author":[{"last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","first_name":"Arseniy","orcid":"0000-0002-2548-617X"},{"first_name":"Alfredo","full_name":"Hubard, Alfredo","last_name":"Hubard"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}],"publication_status":"published","publication":"Topological Methods in Nonlinear Analysis","abstract":[{"lang":"eng","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."}],"date_updated":"2023-08-29T06:32:48Z","volume":53,"type":"journal_article","isi":1,"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"status":"public","page":"457-490","external_id":{"arxiv":["1612.06926"],"isi":["000472541600004"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"department":[{"_id":"HeEd"}],"article_processing_charge":"No","citation":{"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>.","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.","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>","short":"A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490.","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>.","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>","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."},"month":"06","date_created":"2019-07-14T21:59:19Z"}