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Reverse isoperimetric inequality in two-dimensional Alexandrov spaces


Author: Alexander A. Borisenko
Journal: Proc. Amer. Math. Soc. 145 (2017), 4465-4471
MSC (2010): Primary 53C45, 52A40
DOI: https://doi.org/10.1090/proc/13541
Published electronically: April 12, 2017
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Abstract: We prove a reverse isoperimetric inequality for domains homeomorphic to a disc with the boundary of curvature bounded below lying in two-dimensional Alexandrov spaces of curvature $ \geqslant c$. We also study the equality case.


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Alexander A. Borisenko
Affiliation: B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Avenue, Kharkiv, 61103, Ukraine
Email: aborisenk@gmail.com

DOI: https://doi.org/10.1090/proc/13541
Keywords: Alexandrov metric spaces, isoperimetric inequality, $\lambda$-convex curve
Received by editor(s): July 11, 2016
Received by editor(s) in revised form: September 22, 2016, and October 19, 2016
Published electronically: April 12, 2017
Communicated by: Lei Ni
Article copyright: © Copyright 2017 American Mathematical Society

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