--- _id: '1360' abstract: - lang: eng text: 'We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a lower bound for the length of the shortest closed billiard trajectory, related to the non-symmetric Mahler problem. With this technique we are able to give short and elementary proofs to some known results. ' acknowledgement: The first and third authors were supported by the Dynasty Foundation. The first, second and third authors were supported by the Russian Foundation for Basic Re- search grant 15-31-20403 (mol a ved). article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Alexey full_name: Balitskiy, Alexey last_name: Balitskiy - first_name: Roman full_name: Karasev, Roman last_name: Karasev - first_name: Anastasia full_name: Sharipova, Anastasia last_name: Sharipova citation: ama: Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 2016;144(10):4501-4513. doi:10.1090/proc/13062 apa: Akopyan, A., Balitskiy, A., Karasev, R., & Sharipova, A. (2016). Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/13062 chicago: Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/13062. ieee: A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach to closed billiard trajectories in asymmetric normed spaces,” Proceedings of the American Mathematical Society, vol. 144, no. 10. American Mathematical Society, pp. 4501–4513, 2016. ista: Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 144(10), 4501–4513. mla: Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society, vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:10.1090/proc/13062. short: A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American Mathematical Society 144 (2016) 4501–4513. date_created: 2018-12-11T11:51:34Z date_published: 2016-10-01T00:00:00Z date_updated: 2021-01-12T06:50:09Z day: '01' department: - _id: HeEd doi: 10.1090/proc/13062 ec_funded: 1 intvolume: ' 144' issue: '10' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1401.0442 month: '10' oa: 1 oa_version: Preprint page: 4501 - 4513 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Proceedings of the American Mathematical Society publication_status: published publisher: American Mathematical Society publist_id: '5885' quality_controlled: '1' scopus_import: 1 status: public title: Elementary approach to closed billiard trajectories in asymmetric normed spaces type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 144 year: '2016' ...