---
_id: '1330'
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.
article_processing_charge: No
arxiv: 1
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
citation:
  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>
  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>.
  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.
  ista: Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles.
    Israel Journal of Mathematics. 216(2), 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>.
  short: A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845.
corr_author: '1'
date_created: 2018-12-11T11:51:24Z
date_published: 2016-10-15T00:00:00Z
date_updated: 2025-09-22T08:23:27Z
day: '15'
department:
- _id: HeEd
doi: 10.1007/s11856-016-1429-z
ec_funded: 1
external_id:
  arxiv:
  - '1506.06014'
  isi:
  - '000386356400012'
intvolume: '       216'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1506.06014
month: '10'
oa: 1
oa_version: Preprint
page: 833 - 845
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
publication: Israel Journal of Mathematics
publication_status: published
publisher: Springer
publist_id: '5938'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Billiards in convex bodies with acute angles
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 216
year: '2016'
...