Universität zu Köln

Rudolf, Daniel ORCID: 0000-0002-3988-5702 and Krupp, Stefan (2022). A regularity result for shortest generalized billiard trajectories in convex bodies in R-n. Geod. Dedic., 216 (5). DORDRECHT: SPRINGER. ISSN 1572-9168

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Abstract

We study length-minimizing closed generaliceki Euclidean billiard trajectories in convex bodies in R-n and investigate their relation to the inclusion minimal affine sections that contain these trajectories. We show that when passing to these sections, the length-minimizing closed billiard trajectories are still billiard trajectories, but their length-minimality as well as their regularity can be destroyed. In light of this, we prove what weaker regularity is actually preserved under passing to these sections. Based on the results, we develop an algorithm in order to calculate length-minimizing closed regular billiard trajectories in convex polytopes in R-n.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Rudolf, Daniel UNSPECIFIED orcid.org/0000-0002-3988-5702 UNSPECIFIED Krupp, Stefan UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-665407
DOI:	10.1007/s10711-022-00717-3
Journal or Publication Title:	Geod. Dedic.
Volume:	216
Number:	5
Date:	2022
Publisher:	SPRINGER
Place of Publication:	DORDRECHT
ISSN:	1572-9168
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CURVES Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/66540