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Two counterexamples in low-dimensional length geometry
Author(s):
D.
Burago;
S.
Ivanov;
D.
Shoenthal
Original publication:
Algebra i Analiz,
tom 19
(2007),
nomer 1.
Journal:
St. Petersburg Math. J.
19
(2008),
33-43.
MSC (2000):
Primary 51K10, 28A75
Posted:
December 12, 2007
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References:
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- 1.
- A. Besicovitch, On two problems of Loewner, J. London Math. Soc. 27 (1952), 141-144. MR 0047126 (13:831d)
- 2.
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- 3.
- -, On asymptotic volume of Finsler tori, minimal surfaces in normed spaces, and symplectic filling volume, Ann. of Math. (2) 156 (2002), 891-914. MR 1954238 (2003k:53088)
- 4.
- Yu. D. Burago and V. A. Zalgaller, Geometric inequalities, ``Nauka'', Leningrad, 1980; English transl., Grundlehren Math. Wiss., Bd. 285, Springer-Verlag, Berlin, 1988. MR 0936419 (89b:52020)
- 5.
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- 7.
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- 8.
- A. C. Thompson, Minkowski geometry, Encyclopedia Math. Appl., vol. 63, Cambridge Univ. Press, Cambridge, 1996. MR 1406315 (97f: 52001)
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Additional Information:
D.
Burago
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Email:
burago@math.psu.edu
S.
Ivanov
Affiliation:
St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email:
svivanov@pdmi.ras.ru
D.
Shoenthal
Affiliation:
Longwood University, 201 High Street, Farmville, Virginia 23909
DOI:
10.1090/S1061-0022-07-00984-3
PII:
S 1061-0022(07)00984-3
Keywords:
Length metric,
Hausdorff measure
Received by editor(s):
15/FEB/2006
Posted:
December 12, 2007
Additional Notes:
The second author was partially supported by RFBR (grant no.~05-01-00939a)
Dedicated:
To dear Viktor Abramovich Zalgaller on the occasion of his 85th birthday
Copyright of article:
Copyright
2007,
American Mathematical Society
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