{"page":"833 - 845","date_created":"2018-12-11T11:51:24Z","type":"journal_article","article_processing_charge":"No","arxiv":1,"_id":"1330","corr_author":"1","intvolume":"       216","issue":"2","doi":"10.1007/s11856-016-1429-z","date_updated":"2025-09-22T08:23:27Z","title":"Billiards in convex bodies with acute angles","date_published":"2016-10-15T00:00:00Z","abstract":[{"lang":"eng","text":"In this paper we investigate the existence of closed billiard trajectories in not necessarily smooth convex bodies. In particular, we show that if a body K ⊂ Rd has the property that the tangent cone of every non-smooth point q ∉ ∂K is acute (in a certain sense), then there is a closed billiard trajectory in K."}],"acknowledgement":"Supported by People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n°[291734]. Supported by the Russian Foundation for Basic Research grant 15-31-20403 (mol a ved), by the Russian Foundation for Basic Research grant 15-01-99563 A, in part by the Moebius Contest Foundation for Young Scientists, and in part by the Simons Foundation.","main_file_link":[{"url":"https://arxiv.org/abs/1506.06014","open_access":"1"}],"oa":1,"publication":"Israel Journal of Mathematics","publication_status":"published","language":[{"iso":"eng"}],"isi":1,"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"author":[{"orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy"},{"first_name":"Alexey","last_name":"Balitskiy","full_name":"Balitskiy, Alexey"}],"quality_controlled":"1","year":"2016","oa_version":"Preprint","status":"public","publisher":"Springer","scopus_import":"1","ec_funded":1,"day":"15","month":"10","department":[{"_id":"HeEd"}],"external_id":{"isi":["000386356400012"],"arxiv":["1506.06014"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","volume":216,"citation":{"ista":"Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 216(2), 833–845.","ieee":"A. Akopyan and A. Balitskiy, “Billiards in convex bodies with acute angles,” <i>Israel Journal of Mathematics</i>, vol. 216, no. 2. Springer, pp. 833–845, 2016.","chicago":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” <i>Israel Journal of Mathematics</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s11856-016-1429-z\">https://doi.org/10.1007/s11856-016-1429-z</a>.","ama":"Akopyan A, Balitskiy A. Billiards in convex bodies with acute angles. <i>Israel Journal of Mathematics</i>. 2016;216(2):833-845. doi:<a href=\"https://doi.org/10.1007/s11856-016-1429-z\">10.1007/s11856-016-1429-z</a>","apa":"Akopyan, A., &#38; Balitskiy, A. (2016). Billiards in convex bodies with acute angles. <i>Israel Journal of Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s11856-016-1429-z\">https://doi.org/10.1007/s11856-016-1429-z</a>","short":"A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845.","mla":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” <i>Israel Journal of Mathematics</i>, vol. 216, no. 2, Springer, 2016, pp. 833–45, doi:<a href=\"https://doi.org/10.1007/s11856-016-1429-z\">10.1007/s11856-016-1429-z</a>."},"publist_id":"5938"}