Universität zu Köln

Ferone, Vincenzo ORCID: 0000-0003-0997-8390, Kawohl, Bernd ORCID: 0000-0003-2918-7318 and Nitsch, Carlo ORCID: 0000-0001-6673-9332 (2016). The elastica problem under area constraint. Math. Ann., 365 (3-4). S. 987 - 1016. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1432-1807

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Abstract

We show that the elastic energy of a closed curve has a minimizer among all plane simple regular closed curves of given enclosed area , and that the minimum is attained for a circle. The proof is of a geometric nature and deforms parts of in a finite number of steps to construct some related convex sets with smaller energy.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Ferone, Vincenzo UNSPECIFIED orcid.org/0000-0003-0997-8390 UNSPECIFIED Kawohl, Bernd UNSPECIFIED orcid.org/0000-0003-2918-7318 UNSPECIFIED Nitsch, Carlo UNSPECIFIED orcid.org/0000-0001-6673-9332 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-268564
DOI:	10.1007/s00208-015-1284-y
Journal or Publication Title:	Math. Ann.
Volume:	365
Number:	3-4
Page Range:	S. 987 - 1016
Date:	2016
Publisher:	SPRINGER HEIDELBERG
Place of Publication:	HEIDELBERG
ISSN:	1432-1807
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CLOSED CURVES; HEAT-EQUATION; PLANE DOMAINS; CURVATURE; FLOW Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/26856