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Short loops in surfaces with a circular boundary component

Abstract:
It is a classical theorem of Loewner that the systole of a Riemannian torus can be bounded in terms of its area. We answer a question of a similar flavor of Robert Young showing that if S is a Riemannian surface with connected boundary in Rn, such that the boundary curve is a standard unit circle, then the length of the shortest non-contractible loop in S is bounded in terms of the area of S.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1142/S1793525319500602

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
World Scientific Publishing
Journal:
Journal of Topology and Analysis More from this journal
Volume:
12
Issue:
3
Pages:
667-673
Publication date:
2018-09-24
Acceptance date:
2018-07-11
DOI:
EISSN:
1793-7167
ISSN:
1793-5253
Language:
English
Keywords:
Pubs id:
pubs:602029
UUID:
uuid:e9da99ec-a09a-437a-8a1a-35d9a98f52ae
Local pid:
pubs:602029
Source identifiers:
602029
Deposit date:
2018-07-13

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