Duke Mathematical Journal

Area minimizers and boundary rigidity of almost hyperbolic metrics

Dmitri Burago and Sergei Ivanov

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Abstract

This paper is a continuation of our paper about boundary rigidity and filling minimality of metrics close to flat ones. We show that compact regions close to a hyperbolic one are boundary distance rigid and strict minimal fillings. We also provide a more invariant view on the approach used in the above-mentioned paper.

Article information

Source
Duke Math. J., Volume 162, Number 7 (2013), 1205-1248.

Dates
First available in Project Euclid: 10 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1368193652

Digital Object Identifier
doi:10.1215/00127094-2142529

Mathematical Reviews number (MathSciNet)
MR3079248

Zentralblatt MATH identifier
1271.53044

Subjects
Primary: 53C24: Rigidity results
Secondary: 53C65: Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]

Citation

Burago, Dmitri; Ivanov, Sergei. Area minimizers and boundary rigidity of almost hyperbolic metrics. Duke Math. J. 162 (2013), no. 7, 1205--1248. doi:10.1215/00127094-2142529. https://projecteuclid.org/euclid.dmj/1368193652


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